Just for clarity, the overnight entry quota on the NF is 10/day, of which 6 are reservable. The MR might be a bit stiff for someone who has never been off trail before, but I don't know you or your friend, so I won't say anything more.
The standard route up Lone Pine Peak would be very appropriate for a first-time off-trail experience, though it is a bit of a loose slog. You need to pay attention on the descent--the proper route is marked with cairns (or at least it was...), but it isn't hard to get suckered into heading down too soon.
Irvine depends on the route chosen. Getting to the summit block will probably entail more difficult scrambling than anything found on Whitney. The chutes on the east side, if snow-filled, are longer than Whitney. They probably average around 35-40 degrees. Something to consider if conditions are hard and fast.
Another peak to consider would be Langley. Once the approach passes are snow-free (or soft enough to hike safely w/o crampons and axe) it's pretty straightforward. Scrambling up the summit is something you can tune to the level of challenge you feel you are up to, by heading farther west before heading up.
