OCaml - list of lists recursive 'if expression'

I want to create a rec function, say oddleninLdbl, that takes as an argument a list of lists "L" and returns a copy of "L" in which the lists of odd length have been "doubled" - doubled here means the list will concatenate with itself.

To illustrate the above, the idea is to have this :

oddleninLdbl [[]; [5]; [23;5]; [45;65;2]; []; [34;85;7;22;1]];;

returns the following:

[[]; [5;5]; [23;5]; [45;65;2;45;65;2]; []; [34;85;7;22;1;34;85;7;22;1]]

it should also work with whatever list type, again for example this here with strings:

oddleninLdbl [[]; ["mi";"lo"]; ["la"]; ["lo";"co";"mo"]]

should return:

[[]; ["mi";"lo"]; ["la";"la"]; ["lo";"co";"mo";"lo";"co";"mo"]]

I've been running in circles around this one. If I'm not mistaken, I know that my 'if expression' should revolve around something related to the length of the lists within a list, and when it is List.length mod 2 = 1 the sub-list should concatenate with itself.

But, I'm unable to apply it as I've never worked with list of lists! How should this function be written? Your help is much appreciated.