To understand how to solve your problem, I looked at examples foreach, and the second did exactly what you are looking for:
library("foreach")
example(foreach)
foreach(i=1:3) %do% sqrt(i)
Then I adapted this to your problem:
lst <- lapply(1:30, function(x) lapply(1:5, function(y) rnorm(10)))
resFE <- foreach(i = 1:5) %do%
lapply(1:10, function(y) sapply(lst, function(z) z[[i]][[y]]))
Edit: OP was able to find a solution based on my work. Here is the solution:
resFE <- foreach(i = 1:5, .packages = "foreach") %dopar%
{ foreach(m = 1:10) %dopar%
{ foreach(t = lst, .combine = c) %do%
{ t[[i]][[m]] } } }