The main requirement is that application pool account should have read permissions for the AD that is being searched.
SPLMS picker doesn’t do any queries into AD for searching.
It just resolves users already added to site.
I.e. it’s SharePoint that searches for users, then SPLMS handles resolving of members. Picker can be configured which domain it should search – this is standard SharePoint functionality http://technet.microsoft.com/en-us/library/gg602075(v=office.14).aspx