Actually when IGP changes LSPs are not recomputed with LDP or SR-MPLS (when used without TE :).
"LSP" term is perhaps what drives your confusion --- in LDP MPLS there is no "Path" - in spite of the acronym (Labeled Switch *Path*). Labels are locally significant and swapped at each LSR - resulting essentially with a bunch of one hop crossconnects.
In other words MPLS LDP strictly follows IGP SPT at each LSR hop.