There are a number of sources that can be consulted for routes on Lizard Head that likely provide better information regarding things like cam sizes, needed, etc. The following is simply our perspective, written by two people who never considered themselves to be "real" technical climbers.
Let the adventure begin! From the Cross Mountain TH, (#424 to #637 begin hiking across the meadows and head into the forest following the wide and very well-used trail. If you are climbing Lizard Head, you will likely be doing this in the dark, so headlamps will be useful as well as typical approach boots. The trail is never particularly steep. At a little over three miles, the Cross Mtn. trail intersects the Lizard Head trail #505 coming in from the east. Continue WNW to a pass between Lizard Head Peak and Cross Mountain. If heading up to Lizard Head, you may be able to cut up to the west ridge of Lizard Head before reaching the pass. If arriving in the early morning hours, you may have a very good chance of spotting some elk up here. Listen for them and be aware of their scent.
Once you gain the west ridge, follow a use trail as it zig zags up the mostly rocky slope with some tundra interspersed for a while. As you get higher toward the base of the summit tower, almost all vegetation will disappear. Once you reach the cliffs that form the rickety tower, follow at the base of the cliffs to the right (south) until you come to the prominent SW crack to begin the climb. Change into your climbing shoes here, harness up and set up your gear.
The first pitch is rated 5.7+. Some climbers split this into two leads, others one depending on factors like rope length, etc. The distance of this lead is about 155 ft. Some climbers choose to ascend directly up the crack, others begin by ascending the vertical wall just right of the crack for some distance before moving back over into the crack. Somewhere on this wall is an old piton that is still used as an anchor. We went up the wall before entering the crack. Once in the crack, having some skill in managing an off-width crack is useful. The upper crack is about body width. You need to know how to ascend in that situation. We found some of our canyoneering experience to be very useful here.
The first pitch crack ends at a notch that we referred to as a "crow's nest" because it felt like you were in a crow's next on a tall masted sailing ship. On either side it drops off precipitously. There is a large rock horn which everyone uses as a rappel anchor so there were multiple slings on it. There was barely enough room for three people in this notch. From the notch, the second pitch leads off to the north, more or less, and crosses in an upward contour across slopes covered in small scree that would rain down the cliffside. The traverse across this section, while not vertical by any means is made more precarious by the loose scree that covers most everything. There seems to be precious little solid rock to utilize, but fortunately, the going here is only about like a 3rd class scramble. With a good belay from our guide, we were able to move across this section quickly because there's really no climbing involved. To get out of the notch and onto the slope, there's a brief 4th class wall to go up, then you're on the scree slopes. Aim/angle to a crumbly rock overhang at the top of a steep scree slope. The second pitch will end here. Now you can rig up for the third.
Our guide used some features under this overhang to set up an anchor for the next lead using a couple of cams. We could belay from under the overhand and avoid some of the rock that might fall from above. As our guide was heading up setting the route, a near constant stream of small rocks were being rained down on us from above. The protection of the overhang was quite welcome. From the overhang, we climbed up to the left a little to reach the bottom of another crack. About ten feet up there was a "bulge" in the crack that presented something of a bulging overhang. Our guide set up extra protection here in case we needed it. Getting up and over that bulge is what gives this pitch the 5.8 rating. Once above it, we followed the mostly near vertical, body-width crack to it's terminus using technique similar to how we negotiated the crack on the first pitch. At this point we will note that strenuous rock climbing at 13,000 feet is an entirely different game. Combine the technical difficulty with the high altitude and you find yourself exhausted much more quickly. It took each of us about 20 minutes each to work our way up - in part because of a need to stop and catch our breath!
From the end of this pitch, which is in a fairly open spot, the remaining distance to the summit is no more than 3rd class and is basically a walk. Work your way over some rock outcrops, walk around the head of a vertical gully, then scramble on to the summit of more of the same loose, friable rock. With a 4:30 AM start, we arrived at the summit on a typically monsoonal day at 11:15AM. There was not much time to linger because we need to be off the technical portion before afternoon showers would hit and we anticipated they would begin early. This is such an exposed summit, you certainly do not want to be here with any lightening close by. A heavy piece of plumbing pipe held a register in 2012.
To descend, you will definitely need to rappel from the top of the third pitch. This is an airy and spectacular rappel. Enjoy it! Getting back across the second pitch will depend on your own ability to handle the scree-covered slope that could send one plummeting down the cliffs below. Many may want/require a guided set-up to get back down to the top of the first lead. We did not use one. For the final pitch, rappel is required again and it too offers a spectacular view of the terrain well below. You may see hikers down there pausing to watch you on your suicide mission.
Wrap-up: Now you may be asking yourself, "How do I stack up against these people?" So here's an attempt to help you answer the questions, "Can I do this?" and "What would be the best way to go about it?" We never have been what we would call "rock jocks." Though we had some rudimentary rock climbing skills, Tim has probably never led anything more difficult than a 5.6 and prior to this climb, neither of us had ever climbed anything more difficult than a 5.8 and that was in a slot canyon, which is a substantially different environment. Most of whatever skill we had was decades old and there was little by way of the other 13ers to prepare for this. So "how did we prepare?" Our main preparation came from our canyoneering experience. We definitely had rappelling under our belts as well as rope handling skills, knots and stemming skills. That all came in useful. Looking back on the experience, we would suggest anyone attempting this climb whose abilities are questionable should get a months membership in a local climbing gym and reach a point of proficiency where they can climb any of the 5.8 routes comfortably and at least some of the 5.9.
FYI: we contracted a guide through the Telluride Outdoor Adventure School. Our guides name was Keaton and he was a thoroughly prepared and skilled guide and instructor. He/they supplied all the necessary gear including helmets (which we already had), ropes, harware and rock climbing shoes. The service also included a nice trail lunch. We had previously filled him in on what skills and knowledge we had and the result was that Keaton did a great job of quickly assessing our skill level, did not overdo the safety protocols and allowed us to truly participate in the climb. We admit - he did all the leading. We just followed. Having invested about $500 in this guided adventure, we were prepared to make this summit "by hook or crook." Fortunately we did not need either. (We would have spent significantly more than that had we gone out and bought all of our own gear.) We had come prepared with ascenders if we reached a point where we thought we could not successfully free climb the route. We never used them and we never felt a need to have. In getting ourselves over the "bulge" at the third pitch, Keaton had placed an extra piece of webbing that we could use for a handhold if needed. That was the only assist we ever employed. The rappelling was easy and fun. So there you have it. You know how we did it. Now decide how you're going to conquer your own fears and stand on Colorado's most crumbling 13er summit. The links below should offer some additional help. Oh - and one other thing, we climbed Lizard Head at the end of a full week of peakbagging that included a backpack trip up Noname Creek and some moderately difficult summits in the La Platas. Also, we climbed Lizard Head the day after our 34th anniversary.
Links to other information, routes & trip reports for this peak that may be helpful.