Why doesn't my Lemon Posset thicken? What am I most likely doing wrong?
It sounds like your problem is most likely lack of acid. The acid is what causes possets to thicken. That could happen because the lemons aren't acidic enough (maybe the ones you had the first time were more sour). Re-reading your recipe, I notice that there's a second, simpler potential cause: your recipe simply asks for the juice of 1-2 lemons, and you might just have smaller lemons, or drier ones without as much juice.

For comparison, I've successfully made this lime and lemon posset, which uses 5 tablespoons of lemon and lime juice for 2.25 cups of cream. That'd scale to 42 mL of lemon/lime juice for your recipe. If you think you simply didn't have as much juice as before, or that the volume was less than that, I'd start by simply using more lemon juice.

If that's not the problem, and your lemons are for some reason less acidic, then the main option is still to use more lemon juice. Ideally you'd concentrate it, though, so that you don't end up with a smaller fraction of cream in the recipe. You can juice more lemons, then reduce the juice on the stove down to the original volume. (An easier option would be to add extra citric acid to your lemon juice, if you happen to have it.)

(Much of this was said in the comments, but I went ahead and made it an answer - please don't accept it unless you verify it though!)