I actually really like [name_f]Lore[/name_f] for [name_f]Laurel[/name_f]! It feels natural without just turning into [name_f]Lori[/name_f], which I’ve never been keen on either. Lo is sweet as well, and I think [name_f]Lolo[/name_f] has a lovely warm, affectionate feel.
A few more unusual ideas that come to mind are [name_f]Rue[/name_f], [name_f]Elle[/name_f], Rel, and even [name_f]Laure[/name_f]. As a name nerd, I think [name_f]Laurel[/name_f] is one of those names that’s gorgeous in full but surprisingly tricky to nickname, so I’d probably lean towards [name_f]Lore[/name_f] if I wanted something that still felt connected to the original name.