access to the current element of lapply

Dear All,

I would like to use the 'split' function on the dataframe elements  
contained in a list L.

For example :

(df <- data.frame(cbind(c(rep('A',2), rep('B',2)), rep(1:4))))

 X1 X2
1  A  1
2  A  2
3  B  3
4  B  4

(L<-split(df, df$X1))

$A
 X1 X2
1  A  1
2  A  2

$B
 X1 X2
3  B  3
4  B  4

Now, I would like to split EACH data frame, ie, according to column  
2(X2).

lapply(L, split, df$X2)

$A
$A$`1`
 X1 X2
1  A  1

$A$`2`
 X1 X2
2  A  2

$A$`3`
[1] X1 X2
<0 rows> (or 0-length row.names)

$A$`4`
[1] X1 X2
<0 rows> (or 0-length row.names)


$B
$B$`1`
 X1 X2
3  B  3

$B$`2`
 X1 X2
4  B  4

$B$`3`
[1] X1 X2
<0 rows> (or 0-length row.names)

$B$`4`
[1] X1 X2
<0 rows> (or 0-length row.names)


Warning messages:
1: In split.default(seq_len(nrow(x)), f, drop = drop, ...) :
 data length is not a multiple of split variable
2: In split.default(seq_len(nrow(x)), f, drop = drop, ...) :
 data length is not a multiple of split variable



I works but it's dirty.
How  could I do it properly, without warnings and 0 rows data frame  
in output ?
I thought accessing to the current element of 'lapply' to recuperate  
the vector of the column 2 would work.
i.e:

lapply(L,split, L[[current]][,2])


Is there a way to do something like that in R ?


Thanks in advance !

- Martial