I wouldn't have classed Allen as a DM in the classic sense of the word (as classic as a modern football term can be anyway), but more a deep lying ball playing midfielder. Xabi lite is actually fairly accurate.
Lucas however, was definitely a box to box player when he first came. He had been scoring goals, making runs & was regarded as a similar style to Gerrard.
Rafa broke him though. Well, that or he soon spotted that he could dominate here in the same manner so changed his style of play, depends on your opinion of Rafa's man management skills & why he moved players into new positions.