I've driven Lee Vining up over Tioga pass numerous times, but never really paid attention to mileages. My best estimate is:
LV to Tioga Pass gate/entrance to Yosemite: 20 minutes or 15 miles
Tioga pass to Tenaya Lake: another 20 miles or 25 minutes
Total time from LV to Tenaya Lake: 35 miles and around 45 minutes depending on how fast you drive.
I would definitely watch your speed once you enter the Park. LEO's like to hang out on the downhill run from Tioga Pass into Tuolumne meadows and thru the campground/store area.
And I wouldn't expect the 120 to be open until at least Memorial Day...