Is your destination served by LH flights? Assuming that this is an award ticket, they can create award space on their own flights but it's unlikely that a partner would do this to help.

If the destination is Portugal, it's not a huge country; you could fly into Lisbon and rent a car for resorts near Faro. LH probably has a flight to Lisbon and maybe also to Porto, although for Porto you could also fly into some airports in northwestern Spain.