I've been lane swapped against less than a handful of times when going top, so I have very little experience in the matter. But what I can say from experience in one game in particular, I was
against a
top, farming under tower and not doing anything aggressive or risky. That is until one of them went out of lane, then I would take the chance to jump on the lone man and get kills or force them out. If it looked like I had to chase them pretty close to their tower, I would back off early and focus on farming and keeping the wave at my tower. Priority was zoning them out and increasing the gap of exp and gold, not kills. This only happened maybe about 3 times before they caught on and stuck together, but it gave me enough time to stay in lane and farm, while the enemy spent more time out of lane, allowing my team to snowball when we got to teamfighting.
This may not (and most likely does not) accurately portray Jax's strength in a 1v2, or Cait's/Ali's weakness in one, but rather outlines the importance of playing especially safe, and being able to make the best judgement calls relative to your situation.
Beyond that, I would start with champs that have an easy time farming under tower.