The category theory mailing list may be the way to go. Dusko can be annoyed with me for asking the $n+1$th terminological question :-) "Lax products" aren't determined up to iso, but (quick scribbles on back of envelope) up to a "lax iso", that is for any candidates $Z$ and $Z'$ there are morphisms $f : Z \rightarrow Z'$ and $f' : Z' \rightarrow Z$ such that $1 \Rightarrow f;f'$ and $1 \Rightarrow f';f$.

Thanks for the links! Unfortunately, none of these naming schemes lend themselves to a name of the form adjective limit/colimit/product/pullback/etc. Perhaps "locally lax"? Or "univerally lax" to stress that it's the universality of the limit that's being made lax? I note that this is one of the places where the 1-category terminology and the 2-category terminology are in mild conflict: a weak limit weakens the universality of the limit, whereas a lax limit relaxes the cone.

That is indeed what I'm after. The particular case is smash product, but there's obvious generalization to an arbitrary (weighted) limit. Partly my concern is just terminological: I have a paper to write and I need a name for the gadget I have! But I'd also like to make sure it generalizes properly.