Unless there’s a massive heat dome that melts a lot of the snow between now and late July, plan on there being snow and ice on parts of the trail. At the absolute minimum plan on bringing microspikes and gaiters, expect to need crampons and ice axes. You’ll have a better idea of what trail conditions are come early July.
Below are a couple links for checking snow depth. I recommend looking at them frequently in the month prior to your permit date.
Current Snow DepthSNOTEL Sites (Sierra Nevada)
