Mt Irvine (4197m) and Mt McAdie (4206m) are located in the Mt Whitney area of the Eastern Sierra
The Meysan Lakes trail starts from the last Whitney campground before Whitney Portal (at about 2400 meters of elevation).
You have to park the car on the road and walk through the campground,
looking for the trailhead that is actually hidden among summer homes.
If you start hiking before sunrise, this is not trivial at all.
To make matters worse, the trail crosses the paved road one more time: walk
a bit uphill and look on your right for the second start of the trail.
Very long switchbacks (that will be very annoying on the way down) take you around the wall in front of you and into the valley created by the creek that comes down the lake. The trail ends at a meadow. Continue in the same direction (roughly south) and enter the lake from the west.
Mt Irvine is the prominent peak to the west of the Meysan lakes but what you see from the lake is a false summit.
Looking south from the lower lake:
Looking west from the upper lake:
Mt Irvine can be climbed from the western side of the lake along the chute that splits but either way terminates exactly at the summit. This is mostly class 2. The same chute can also be used to reach Mt Mallory.
The other way to reach the summit (not recommended unless there is snow/ice in the chute) is via the southeastern ridge, which is a series of false summits. Leave the trail just when the trail starts going down and climb the mountain to your right. That is the first of many false summits. A tiny pass leads you to the western side of the mountain and now you can see all the other false summits. the real summit is in fact barely visible. You have to follow the crooked ridge created by these false summits until there are no more peaks to climb! It easily takes 2 hours from the first false summit (the one you see from the lakes) to the real summit.
One can also climb Mt Irvine from Arc Pass via Consultation Lake (possibly the easiest route) but that requires a Whitney Zone permit. The bureaucracy that is paid to protect you has a unique way to make simple things complicated and dangerous.
McAdie has two obvious summits, the higher being the northern one. It is trivial to descend from Mt Irvine to Arc Pass. It is not trivial to climb Mt McAdie. The east face (facing Mt Irvine) is tough without a rope and requires skills in route finding. Mt McAdie is easier from Crabtree Pass (the west face, facing Mt Whitney) but that implies a longer approach. After rounding Crabtree Pass one can easily climb to the notch between the north and south summits. Just before the notch there is a way to move left and start climbing rocks directly to the northern summit. You could also reach the west face of Mt McAdie from Consultation Lake, ideally via Whitney Pass (faster and safer), but that requires the permit for the Whitney Zone; and, again, bureaucracy doesn't really like that you hike safely.
Mt Mallory (4221m) is an easy detour from Mt Irvine.
If you want to do an epic loop, climb Mt Irvine, descend on Arc Pass, climb Mt McAdie, descend to Consultation Lake and then cross over to the Meysan Lake trail via an unnamed pass.
But, yet again, if you do this, you'll be briefly in the ridiculous Whitney Zone, for which you need a permit.