Apply arbitrary function that returns a list to vector in R

I recently asked a similar question (link), but the example that I gave there was a little too simple, and the answers did not work for my actual use case. Again, I am using R and want to apply a function to a vector. The function returns a list, and I want the results to be formatted as a list of vectors, where the names of the output list correspond to the names in the list returned by the function, and the value for each list element is the vector of values over the elements of the input vector. The following example shows a basic set up, together with two ways of calculating the desired output (sum.of.differences and sum.of.differences.2). The first method (sum.of.differences) seems to be the easiest way to understand what the desired output; the second method (sum.of.differences.2) avoids two major problems with the first method -- computing the function twice for each element of the input vector, and being forced to give the names of the list elements explicitly. However, the second method also seems relatively complicated for such a fundamental task. Is there a more idiomatic way to get the desired results in R?

x <- rnorm(n = 10)
a <- seq(from = -1, to = +1, by = 0.01)

sum.of.differences.fun <- function(a) {
  d <- x - a
  list(
    sum.of.absolute.differences = sum(abs(d)),
    sum.of.squared.differences = sum(d^2)
  )
}

sum.of.differences <- list(
  sum.of.absolute.differences = sapply(
    X = a,
    FUN = function(a) sum.of.differences.fun(a)$sum.of.absolute.differences
  ),
  sum.of.squared.differences = sapply(
    X = a,
    FUN = function(a) sum.of.differences.fun(a)$sum.of.squared.differences
  )
)

sum.of.differences.2 <- (function(lst) {
  processed.lst <- lapply(
    X = names(lst[[1]]),
    FUN = function(name) {
      sapply(
        X = lst,
        FUN = function(x) x[[name]]
      )
    }
  )
  names(processed.lst) <- names(lst[[1]])
  return(processed.lst)
})(lapply(X = a, FUN = sum.of.differences.fun))