It looks like X1, X2 etc are indexes or keys of some kind... is that right? You're using a list like a dictionary-like data structure. If that's the case you probably want to use Associations instead of lists. Associations are the correct datastructure for this situation. You can solve this issue with Merge:

Merge[{<|a -> 1, b -> 2|>, <|a -> 4, b -> 5|>}, Apply[Times]]

Here "a" and "b" are the keys. We merge them and Apply Times.

For lists, it's not clear how you want to handle edge cases, but you can do the following:

Transpose[{L1[[All, 1]], L1[[All, 2]]*L2[[All, 2]]}]

{{X1, y1 z1}, {X2, y2 z2}, {X3, y3 z3}, {X4, y4 z4}}

I'll let you put together how that works.

sorry. missed the answer:

In[57]:= Transpose[{Transpose[L1][[1]], 
  Transpose[L1][[2]] Transpose[L2][[2]]}]

Out[57]= {{X1, y1 z1}, {X2, y2 z2}, {X3, y3 z3}, {X4, y4 z4}}

Yes. Just try it.

But note, the code given by Sean Clarke,

Transpose[{L1[[All, 1]], L1[[All, 2]]*L2[[All, 2]]}]

which is basically the same, looks a bit mor elegant.

Regards HD