Stropping, in general, will be much more effective if the edge is sufficiently prepared beforehand. In other words, the more you can do with your hones ahead of time, the more effective the pastes & strop will be. Make sure the edge is fully apexed (burr formed along the full length of the edge) with the coarse hone on your Lansky, before proceeding to the next hone. Then, use the subsequent hones to gently reduce the burr and refine the edge. I HIGHLY RECOMMEND a good magnifier (at least 10x) to inspect the edge under BRIGHT LIGHT, as you work. That's the best way, by far, to be absolutely sure you've done all you can with the hones, before stropping.
I have two Lansky kits, the 'Deluxe' and the diamond kit. The Deluxe kit uses the standard hones, including two ceramics (purple stone in blue holder, and white stone in yellow holder). The two ceramics, in my opinion, would help a lot after the fine diamond hones in your kit. Those two will begin to produce some mirror polish on the edge. I don't think stropping with the diamond pastes, after your finest diamond hone, will fully polish your edge. If you're not concerned about the full mirror polish, that's OK. The diamond pastes, at 6/3/1 micron, are a pretty big jump down in grit size after the fine diamond hone, so they'll work more to polish the 'teeth' on the relatively coarse edge left by the Lansky diamond hones. With your current set of hones, I don't think you'll benefit much by going smaller than the 1 micron paste.
As for the bare leather stropping, it CAN take your edge further. But this is where it's the most important to make sure you've fully prepared the edge beforehand. Point being, the ultra-fine silicates in the bare leather are SO SMALL (0.01 micron, maybe smaller), if the edge isn't ready for it, you won't likely notice much improvement in polish or sharpness (aside from burr removal, if there's any burr left on the edge). If you can notice immediate improvement in sharpness, after maybe 10 passes on the bare leather strop, you know you've done it right. If you just keep stropping & stropping, and don't notice much improvement, then it's likely that not enough work was done prior, with the hones. The better you get at fully utilizing the hones beforehand, the more you'll find that the edge can be significantly improved by stropping on many different media (like bare leather, or newsprint, or even on your jeans). It's a very satisfying feeling, when you've begun to notice this.