Are you sure this is their current position?
The LP got taken over by Mises faction and a lot of policies have changed
You didn’t provide a date or link for this policy on immigration so I need to see that
They quit posting the full text version years ago and this is all they will say since.
“3.4 Free Trade and Migration
We support the removal of governmental impediments to free trade. Political freedom and escape from tyranny demand that individuals not be unreasonably constrained by government in the crossing of political boundaries. Economic freedom demands the unrestricted movement of human as well as financial capital across national borders.”