55-57cm top tube (or effective top tube.)
Right. I'm 5'11", long legs, relatively short torso, I am fine with a 56-57cm effective top tube which is typical for 56-57cm frames (90% of them are 56cm, 57cm is an oddball size). But your friend could need a 59cm top tube if he has more typical proportions than me, which could even push him up to a 58cm. Lance was 5'11" and rode a 58cm, I presume he needed the longer top tube.
Seat tube length is rather irrelevant. EFFECTIVE TOP TUBE length is what will determine your reach on the bars and your position on the bike, that's really the key dimension 90%+ of the time for most cyclists. My MTB has an 18" seat tube (very short, I needed a longer 400mm stem to get the bike to fit) but the effective top tube is that 57cm number, which is perfect.