The East Face route is (shockingly enough) approached from the east side of the formation. Specifically, drive highway 20 to the Washington Pass Overlook turn-off (that's approximately 0.75-1 mile east of the Blue Lake trailhead turn-off). From the overlook turn-off, continue east on highway 20 for approximately 300-400 yards. If you look carefully, you'll see a small pond on the right (south) side of the highway just past the overlook. Just east of the pond there is a wide paved pull-off on the left (north) side of the highway. Park your car here. Note that this is several hundred yards west of the haripin turn. Alternatively, you could also park your car at the Blue Lake trailhead or somewhere at the overlook access road or parking area (overlook is seasonally gated though). This latter alternative leaves you with less road hiking after your climb.
Regardless of where you choose to park, hike the highway to the little pond mentioned above. Pick up a well-beaten climbers' trail at the east end of the pond (take your time - once you find it, it's nearly impossible to lose!). Note that this is the standard trail used for accessing most routes on the east side of Liberty Bell Group with the exception of routes on the east faces of South and North Early Winter Spires (which are accessed from the hairpin turn further east). Hike the trail as it climbs steeply through timber. In about 30 minutes you'll come to the edge of a large boulder/scree field lining the eastern base of Liberty Bell, Minuteman, and Lexington Towers. Boulder hop up towards the base of Liberty Bell (look for the characteristic Lithuanian Roofs 200 feet above ground on Liberty Bell's east face marking the Liberty Crack route). Traverse left (~south) passing Liberty Bell and Minuteman Towers. Immediately past Minuteman (separated from east face of Lexington by a narrow gully), stop and make some decisions.
Option one is to start the climb up the low angle slabs and dihedral on the right side of Lexington's east face. This worked for us as it bypassed the snowfield at the base of Lexington. Option two is to traverse further south (along eastern base of Lexington) to the next gully (on left side of Lexington's east face). Climb slabs just right of that gully. Whichever route you decide on, they both merge atop a class 3 ledge system ~100 feet above the base.
This is a great route on amazingly solid rock that (acc. to Nelson and Potterfield's guidebook) does not reach the summit of Lexington due to poor rock on the east/south faces of Lexington's summit spire (for that see the North Face route).
Pitch 1:Option 1. 5.6, 200 feet. Start climbing up low angle slabs immediately left of the gully separating east face of Lexington from Minuteman Tower. Enter a low angle dihedral just above and move left about 100 feet above ground onto a class 3 ledge system (small trees). Traverse ledge system left until you're out of rope. Belay. Option 2. 5.? (probably easy), 150 feet. This is untested but alternatively you could traverse the snowfield at the base of the east face left to the next gully system (left of Lexington's east face). Book (Nelson and Potterfield) claim 3rd class scrambling brings you to the right side of the same ledge system as described above.
Pitch 2: 5.7-5.8, 200+ feet. Even though this pitch is relatively easy, it has some spicy runouts to keep things interesting. From near the left end of the class 3 ledge system, move up via ledgy slabs looking for the most protectable and easiest way. Much of the rock is nicely devoid of cracks and you might find yourself pulling 5.7-ish moves well out of sight of your last piece. Going eases on the upper half of pitch. Belay when out of rope (terrain becomes ledgy higher up - many options possible). Key here is that you're near the left side of the east face.
Pitch 3: 5.6, 120 feet. Continue moving up looking for the easiest line and generally keeping to the left side of the face. Belay at the base of an obvious and large, left-facing dihedral. Decent belay stance. Note that you might want to stretch this pitch to the top of the dihedral where you'll have a good ledge with a tree on the right (we did not do this and had to really stretch the 60 meter ropes on the next pitch).
Pitch 4: 5.8, 200+ feet. Climb the above mentioned dihedral (5.7-5.8) - might want to start just left of the initially chossy dihedral up a nice flake of rock and then move into the dihedral. Above this initial dihedral you pass a small ledge and enter another left-facing dihedral (with seasonal tufts of grass). Beautiful hand/off-hands crack brings you to the lower roof. Undercling and traverse left under the roof (5.8) and move up a third dihedral (low angle). Belay 10 feet up this dihedral (piton and good gear; semi-hanging) 30 feet below the largest of the roofs (with the prominent chimney on the right).
Pitch 5: 5.9, 120 feet. Move up the low angle but awkward dihedral to reach a stance in the mouth of the prominent chimney right of the huge roof. You're not climbing this chimney. Instead, move right onto a face with a good horizontal crack/ledge system. Foot shuffle rightwards along this mini-ledge (5.8) for about 20 feet until you reach a flake in the face. Move up the flake (nice solid 5.9; Becky's guidebook calls this 5.9+). Initially a wide crack which quickly narrows down to fingers (crux of route perhaps). Few moves and the crack widens to hand jams. Near top move left onto a good stance below an obvious wide crack (with a 2X4 fixed inside).
Pitch 6: 5.9, 200+ feet. Move up the wide crack (5.9) clipping the fixed piece of 2X4 inside. Crack will take a tipped out #5 Camalot in places. There are 2 new bolts right next to each other (what gives?) about 20 feet up. 30 feet higher you enter a 5.7 chimney - easier going but no pro. Twin hand crack system follows the chimney which in turn is followed by more wide cracks (5.8-ish according to Becky) and chockstones (big and small). Near the end of your rope (as angle eases) move left out of the wide stuff and onto a sandy ledge with a thick tree. Belay.
Pitch 7: 5.6, 200 feet. Make your way up and right over easier terrain (much 4th class with some mid-5th steps). Belay on a nice wide ledge with a view of the summit spire above you.
Pitch 8: 4th class, 150 feet. Walk westward along a wide catwalk. Smear a low angle slab on the right side of a hump. Belay in the sandy notch at the base of Lexington's summit spire.
Descent: Scramble down the very loose and dirty gully system near the southern base of Lexington's summit spire. The narrow gully that hugs the base is probably too steep. Take the next gully on the left (class 3 - loose!). Few hundred feet below top of notch, you might have to do a short (~30-40 foot) rappel (or it might be downclimbable - not sure). Continue down the gully hiking westward till you pick up the climbers' trail system on the west side of Liberty Bell Group.
Follow the trail down to the main Blue Lake Trail and hike the trail back down towards the road. About 0.25 miles before you reach the trailhead, you'll notice the highway about 200 yards beyond the trees. Nice shortcut boot path takes you to the highway. Hike the shoulder back to your car.