I discovered experimentally that a certain finite poset (sorry, I cannot give its definition here) seems to be in fact a (non-distributive, non-graded) lattice. The covering relations are reasonably simple, but it seems not so easy to find out whether one element is smaller than the other, let alone find the meet (or join) of two elements. However, it is (relatively) easy to see that the poset has a minimum and a maximum.

I wonder whether there are standard techniques for proving that a poset is a lattice, that do not need knowledge about how the meet of two elements looks like. (In fact, any example would be very helpful.)

Some more hints:

I don't see a way to embed the poset in a larger lattice...

the poset is (in general) not self-dual, but the dual poset is itself a member of the set of posets I am looking at.

to get an idea, here is a picture of one example (produced by sage-combinat and dot2tex)