We've been there the first week of June, mid June and the first part of July. During the early part of June it's still very much the changing of the season IMO thus, your going to probably get a lot of different opinions on what the weather is like. During our week we had very warm days and one morning where is snowed on us but, we were staying at the Ridge Tahoe up in the mountains. The snow stuck for a little while, wasn't much accumulation and melted off by late morning/early afternoon if memory serves me correctly. At least I know it didn't stick around long.
Temps will vary greatly from down by the lake to up on the mountains. I believe at Timber Lodge you can probably count on high's in the 60's to 70's during the days with evening temps that might require a lite jacket.
Personally, I find it to be a very nice time to Visit Lake Tahoe but then again, we enjoy temps that are slightly cooler.