I left at Trail camp at 0400 on the 16th. Sun was rising when I hit trail crest. Summited at 0730. So, 3 and a half hours for me to reach the summit. I'm about 40 pounds overweight and went pretty slow and steady.
Good job, but that pace isn't typical for someone in your condition. I carried a light pack from Trail Camp (under 15 pounds), am in pretty decent shape (ran a 5:15 mile or better several times this year), and it still took me more than 4 hours to reach the summit from Trail Camp. I could probably have gotten there in 3 and a half hours if I had to, but that pace would have left me exhausted with no time to enjoy the view and take pictures.
Anyway, on July 20th, the sun rose over the horizon at 5:44 (viewed from ~13,000'), but it was bright enough to see the outline of the landscape around an hour before at 4:45. You can look at the sunrise/sunset times for Lone Pine on different dates and adjust accordingly: