I would imagine that only your doctor can tell you that. They might want you to have a stress test first, depending on your other physical conditions and/or meds.
There's a formula to follow:
Max HR = 220-age
For aerobic exercise the advisable range is 60-80% of max HR, but it all depends on the individual. Some people reach a HR of 200bpm and are fine. In my opinion, I think as long as you're asymptomatic you're ok, but it wouldn't hurt to consult with your doctor.
Umm, this is a liver TRANSPLANT patient you are talking to! They are also diabetic! Transplant patients are on potent meds and are also likely to have other serious conditions along with it. And diabetic patients are way more likely to have heart disease than non-diabetics, so please don't blithely tell them that it would be ok as long as they are not having symptoms.