Lord Henshingly Croft
From WikiRaider
Lord Henshingly Croft is Lara's deceased, former archaeologist father, according to the Games. In the Tomb Raider Comics they used the same name, but in the Movie they "changed" his first name to Richard. In any case, he was married to Lady Amelia Croft, Lara's mother.
There is also a slight chance that Henshingly is part of the family name. I found no official data stating one or the other as fact. So for all we know his name might be Lord Richard Henshingly Croft.