Our lime is having doing the opposite and fruiting a massive amount so ill let you know what we've been doing in case any if it helps

It's in a pot so needs a bit of different care to a ground planted tree but here goes. It gets seasol once a fortnight when the veggies are fed. Rooster booster once every three or four weeks, a liquid iron supplemenr once every six weeks or so and a designated citrus feed every three or four months. It seems like a lot I know, but because everything here is in pots we take extra care with them I guess. It's obviously paying off as the last time I checked one branch has something like 50 small limes starting out. The tree is only about 1.3m high...

Given yours is planted near your lemon it may be that the lemon, as the stringer tree, is sucking nutrients from the ground that the lime needs. So you may need to supplement a bit to help it set fruit.

As for the jasmine, give it a hair cut. Big time. See what happens. If its not flowering it may just keep growing out of control if you don't hard prune it. Hate the stuff. Lovely to look at bit can get out of control so easily and I am highly allergic. We had to rip out fenced to get rid of it at our last house as it had wound itself so tightly around it. Once we realised that was my allergy trigger...