From Toulumne Meadows, follow the JMT for 11.3 miles. Leave the trail before it makes its descent to cross the creek for the last time, about a mile below Donohue Pass. You can see Mt. Lyell to the SW from this point. Follow the canyon south, then southwest as it climbs over granite ledges and benches. This climbing is enjoyable with solid rock.
The Lyell Glacier is split by a large buttress. Head for the lower part of this buttress which provides access to the base of the Lyell Glacier.
An alternative approach to the Lyell Glacier is offered by mlog:
If you don't want to follow the standard route up the slabs and snow to reach the Lyell glacier from JMT, you can leave JMT earlier, climb up the North-North East ridge of Maclure, and follow it to the western side of the Lyell glacier right below the Lyell-Maclure saddle. This route offers nice Class 2-3 scramble and incredible views of Lyell and Maclure from the North side. Here is the short description of this approach:
After the river crossing (Lyell fork of Tuolumne River) at the Mile 160 mark on JMT, follow JMT up the headwall for ~300 vertical feet. Once headwall is reached and you are in the small meadow, leave JMT and turn right towards the obvious saddle. Scramble easy Class 3 boulders to the saddle. It will take you to the bigger meadow with a couple of lakes. From here you should see the view of Lyell, Maclure and the entire Lyell Glacier for the first time since the Lower Lyell Canyon. Cross the creek and scramble up Class 2 - easy Class 3 boulders to the North-North East ridge of Maclure. Follow the ridge until you get to the bottom of the big buttress (orange rock) immediately to the North of Maclure. Stay on the left of the buttress and climb around (easier on the right side) two small lakes to reach the Lyell Glacier below the Lyell-Maclure saddle. From here you can either ascend the saddle, traverse the glacier to the East Arete route or follow any other glacier route variation depending on the glacier conditions and your equipment.
Due to changing snow conditions from year to year, there are many variations that can be used to gain access to the summit. The three common ones are presented here.
In high snow years, or early in the season, the East Arete provides the most direct access to the summit with the least amount of snow travel. Climb to the right of the buttress that splits the Glacier, as far as needed to ensure soft snow (in the morning hours the left hand side is shaded by the buttress and may be quite hard). At the ridge, climb class 3 rocks to the summit. In low snow years or late in the season, this route can be considerably harder. On a second attempt I was rebuffed by a gaping bergschrund (which was just passable) and loose, crappy class 5 rock which forced a retreat.
This is the low point between these two prominent peaks, and usually the easiest route to the summit. From the col, climb the glacier until you can exit onto class 2-3 rocks to the right.
This is the central chute just right of the summit. In low snow years it provides an alternative if the East Arete proves too difficult (and keeps you from having to climb all the way down to the Lyell-Maclure Col). A bergshrund may be present, though it seems to usually be worse between this point and the East Arete. Follow the snow up as far as you can (until it runs out or becomes ice), then exit to the right on class 3 rocks. You may be able to follow the chute directly up (keeping right of the ice in the center), or may have to climb more difficult class 3 more to the right.
There are several summits once you reach the top. The one to the SE is the highest.
Axe and Crampons recommended. A number of parties climb via the Lyell-Maclure Col without these, but the rocks here are class 3-4. Having crampons and axe provides more options, and is safer than going without.
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