applying cbind (or any function) across all components in a list

I'm confused why I haven't made clear what I am asking for help with.  

I have two different lists with two (or many) components, [[1]] and [[2]]. 
One of the list has components with dim=c(2,3) and the other has dim=c(2,2). 
I want to create a new list with components dim=c(2,4) by binding together
the averages of the columns using

cbind((l1[[1]][,1]+l2[[1]][,1])/2, (l1[[1]][,2]+l2[[1]][,1])/2,
(l1[[1]][,2]+l2[[1]][,2])/2, (l1[[1]][,3]+l2[[1]][,2])/2)

which should put out:

     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    2    3    4    5

my problem is finding out how I can apply this function to all the
components within the list in the same function.

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