So, must a posset be made with citrus juice in order to set up?

Well, both the posset and syllabub are deserts created by curdling milk or cream with an acid of some sort. Traditionally it was done by adding ale or wine, later this was changed to using lemon juice as the curdling agent. The key element is the acid which reacts with the milk proteins. It's just smoother with cream, thanks to all the fat. I suppose you could use a bit of cream of tartar to replace the lemon juice, as it will produce a stabilized whipped cream. I don't use it that way myself, so I couldn't say what effect it would have on the taste of your final product. I also wonder if perhaps what you had was a mixture of a lavender infused vodka and cream- which might well thicken somewhat into a drinkable desert? The only real way to get an answer would be to ask the restaurant where you had it. They may be able to put some light on the matter for you. If you are fortunate, they might even share the recipe.