Several different routes are described on the web for climbing to the lakes beneath Granite Dome. I believe the route described here is the easiest for reaching Iceberg, Sardella, Ridge, and upper Lewis lakes. It is off-trail and there is a small amount of scrambling; however, this is mostly just a hike with no dangerous exposure, assuming the right route and no snow. After the snow has melted, it would not be difficult to reach Granite Dome from this route.
The route leaves the Huckleberry Trail
just above the fork between Summit Creek and Lewis Lakes Creek. This is just over seven miles from Kennedy Meadows at an elevation of about 7300 feet. Cross both creeks, and head up the wide canyon west of the trail. By staying a little high on the north side of the canyon, you can avoid the downed trees in the forested sections and hike in almost a straight line to the gap at the top of the canyon. There are many cairns. After you find one, they should help you stay on the best route. The canyon becomes steep and has a low cliff at the top. The easiest way to climb the cliff is on the far right side of the gap. None of the lakes are visible from the top.
To reach Sardella, drop a little from the gap and then contour to the southwest taking advantage of several wide ledges. When you reach the grassy and flowery stream coming down from Sardella Lake, follow it up to the lake.
From Sardella, there is a short draw leading to upper Lewis Lake. This lake is in a granite cirque directly below Granite Dome. The easiest way up the north side of Granite Dome is to climb up the ridge west of upper Lewis Lake. I did not try it, because there were still patches of deep snow.
Return back to Sardella Lake. As you begin to drop down the outlet stream, you'll see a long, 30-50 foot cliff of granite dropping down to the northeast. To get to Ridge Lake, climb this cliff as soon as you can, not very far below Sardella Lake. You can then hike down along the top of the cliff until you reach the north end of Ridge Lake.
From there, you can continue northwest to Iceberg Lake. The north end of Iceberg has a great view overlooking Relief Valley and East Flange Rock.
Return back to the north of Ridge Lake and climb down the steep 50-foot slope. You should see a cairn marking the way down the slope. From the bottom, you can reach the ledges that lead back the way you came, to the gap and on down to Summit Creek.