Which Tomb Raider game are you talking about? If the original (1996), I did at some point reconfigure the controls for the Logitech F310 gamepad (GOG version), and I recall it working great. It took some time though to configure all important controls to the gamepad as there are quite many actions you want to put into it, but I recall I got a configuration I was happy with. Then again, I didn't see a real benefit with using a gamepad either, so in the end I ended up playing it with a keyboard anyway...

Naturally the Playstation version worked with the Playstation gamepad too... :)

Also, what you described doesn't really fit into the 1996 version of Tomb Raider, as the correct way to jump was to walk slowly to the edge, back up a bit, and then run&jump. Then you'd always get a perfect jump each time, Lara would jump exactly at the edge, you didn't need to time it yourself.

There were a couple places though in TR where you didn't have time to do that, but had to make series of running jumps in a quick succession. But for the most part, that's how I did the jumps in TR. I guess the controls changed in the later TR games though. I think at least the first three TR games worked pretty much like that, though.