Splitting and manipulating nested lists

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I'm trying to split a nested list by a group variable. Please consider the following structure:

> str(L1)
List of 2
 $ names:List of 2
  ..$ first: chr [1:5] "john" "lisa" "anna" "mike" ...
  ..$ last : chr [1:5] "johnsson" "larsson" "johnsson" "catell" ...
 $ stats:List of 2
  ..$ physical:List of 2
  .. ..$ age   : num [1:5] 14 22 53 23 31
  .. ..$ height: num [1:5] 165 176 179 182 191
  ..$ mental  :List of 1
  .. ..$ iq: num [1:5] 102 104 99 87 121

Now I need to produce two lists, which use both L1$names$last to splice, resulting in L2 and L3, seen below:

L2: Result grouped by L1$names$last

> str(L2) 
List of 3
 $ johnsson:List of 2
  ..$ names:List of 1
  .. ..$ first: chr [1:2] "john" "anna"
  ..$ stats:List of 2
  .. ..$ physical:List of 2
  .. .. ..$ age   : num [1:2] 14 53
  .. .. ..$ height: num [1:2] 165 179
  .. ..$ mental  :List of 1
  .. .. ..$ iq: num [1:2] 102 99
 $ larsson :List of 2
  ..$ names:List of 1
  .. ..$ first: chr [1:2] "lisa" "steven"
  ..$ stats:List of 2
  .. ..$ physical:List of 2
  .. .. ..$ age   : num [1:2] 22 31
  .. .. ..$ height: num [1:2] 176 191
  .. ..$ mental  :List of 1
  .. .. ..$ iq: num [1:2] 104 121
 $ catell  :List of 2
  ..$ names:List of 1
  .. ..$ first: chr "mike"
  ..$ stats:List of 2
  .. ..$ physical:List of 2
  .. .. ..$ age   : num 23
  .. .. ..$ height: num 182
  .. ..$ mental  :List of 1
  .. .. ..$ iq: num 87

L3: Each group only permits one occurrence of L1$names$last

List of 2
 $ 1:List of 2
  ..$ names:List of 2
  .. ..$ first: chr [1:3] "john" "lisa" "mike"
  .. ..$ last : chr [1:3] "johnsson" "larsson" "catell"
  ..$ stats:List of 2
  .. ..$ physical:List of 2
  .. .. ..$ age   : num [1:3] 14 22 23
  .. .. ..$ height: num [1:3] 165 176 182
  .. ..$ mental  :List of 1
  .. .. ..$ iq: num [1:3] 102 104 87
 $ 2:List of 2
  ..$ names:List of 2
  .. ..$ first: chr [1:2] "anna" "steven"
  .. ..$ last : chr [1:2] "johnsson" "larsson"
  ..$ stats:List of 2
  .. ..$ physical:List of 2
  .. .. ..$ age   : num [1:2] 53 31
  .. .. ..$ height: num [1:2] 179 191
  .. ..$ mental  :List of 1
  .. .. ..$ iq: num [1:2] 99 121

I`ve tried to apply this solution, but it appears that this won't work for nested lists.

Reproducible code:

L1 <- list("names" = list("first" = c("john","lisa","anna","mike","steven"),"last" = c("johnsson","larsson","johnsson","catell","larsson")),"stats" = list("physical" = list("age" = c(14,22,53,23,31), "height" = c(165,176,179,182,191)), "mental" = list("iq" = c(102,104,99,87,121))))

L2 <- list("johnsson" = list("names" = list("first" = c("john","anna")),"stats" = list("physical" = list("age" = c(14,53), "height" = c(165,179)), "mental" = list("iq" = c(102,99)))), "larsson" = list("names" = list("first" = c("lisa","steven")),"stats" = list("physical" = list("age" = c(22,31), "height" = c(176,191)), "mental" = list("iq" = c(104,121)))), "catell" = list("names" = list("first" = "mike"),"stats" = list("physical" = list("age" = 23, "height" = 182), "mental" = list("iq" = 87))))

L3 <- list("1" = list("names" = list("first" = c("john","lisa","mike"),"last" = c("johnsson","larsson","catell")),"stats" = list("physical" = list("age" = c(14,22,23), "height" = c(165,176,182)), "mental" = list("iq" = c(102,104,87)))), "2" = list("names" = list("first" = c("anna","steven"),"last" = c("johnsson","larsson")),"stats" = list("physical" = list("age" = c(53,31), "height" = c(179,191)), "mental" = list("iq" = c(99,121)))))

EDIT: Please note that the actual dataset is quite large and more deeply nested than the provided example.

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