A reproducible example would be nice to illustrate your problem, since you didn't give us such example I just assume a List and made some replications
List <- list(c(2,1,3,4,5,6), c(1,4,5,7,0,6), c(2,4,7,9,3,1))
set.seed(001)
replicate(3, lapply(List, sample, 7, replace=TRUE), simplify = FALSE)
which produces
[[1]]
[[1]][[1]]
[1] 1 3 4 6 1 6 6
[[1]][[2]]
[1] 7 7 1 4 4 0 5
[[1]][[3]]
[1] 3 7 3 1 7 3 1
[[2]]
[[2]][[1]]
[1] 1 4 2 1 3 2 3
[[2]][[2]]
[1] 6 5 5 7 5 4 0
[[2]][[3]]
[1] 3 3 2 3 7 3 9
[[3]]
[[3]][[1]]
[1] 5 4 4 5 2 3 5
[[3]][[2]]
[1] 0 5 6 5 4 1 1
[[3]][[3]]
[1] 4 9 9 7 1 4 7
Note that this approach will give you a resampled data (with replacement) for each element of your original list, that's why each replication is a list consisting in three elements each one.
If you write sapply instead of lapply inside replicate(...) the resulting output would be nicer.
set.seed(001)
replicate(3, sapply(List, sample, 7, replace=TRUE), simplify = FALSE)
[[1]]
     [,1] [,2] [,3]
[1,]    1    7    3
[2,]    3    7    7
[3,]    4    1    3
[4,]    6    4    1
[5,]    1    4    7
[6,]    6    0    3
[7,]    6    5    1
[[2]]
     [,1] [,2] [,3]
[1,]    1    6    3
[2,]    4    5    3
[3,]    2    5    2
[4,]    1    7    3
[5,]    3    5    7
[6,]    2    4    3
[7,]    3    0    9
[[3]]
     [,1] [,2] [,3]
[1,]    5    0    4
[2,]    4    5    9
[3,]    4    6    9
[4,]    5    5    7
[5,]    2    4    1
[6,]    3    1    4
[7,]    5    1    7