lapply version with [ subseting - a suggestion

Dear R developers,

Reviewing my code, I have realized that about 80% of the time in the lapply I
need to access the names of the objects inside the loop.

In such cases I iterate over indexes or names:
lapply(names(x), ... [i]), 
lapply(seq_along(x),  ... x[[i]] ... names(x)[i] ), or
for(i in seq_along(x)) ...

which is rather inconvenient.

How about an argument to lapply which would specify the [ or [[ subseting to use
in the splitting of the vector?
Or may be a different set of functions lapply1,
sapply1?

I believe this pattern is rather common for other users as well.

Thanks.
VS.