The author deals with a problem stemming from a boundedness question for torsion modules and its translation into ideal lattices. The results are part of a round trip from torsion modules to ultrafilters through lattices. The starting point was a problem on torsion modules over commutative integral domains. It is shown that the lattices which are transversally but not uniformly bounded, corresponded to certain ultrafilters with peculiar boundedness properties similar to those studied by Ramsey. The prototypical candidates of the two types of lattices which one is led to construct from ultrafilters appear to be of interest beyond the original questions.