Completed articles on Lawrence? Ask for more (2,3,4)
I believe the answer is:
up the ante
'ask for more' is the definition.
(upping the ante is asking for more excitement)
'completed articles on lawrence?' is the wordplay.
'completed' becomes 'up' (up can mean completed or finished).
'articles' becomes 'the an' (indefinite article 'the', definite article 'an').
'on' means one lot of letters go next to another.
'lawrence?' becomes 'TE' (initials of TE Lawrence aka Lawrence of Arabia).
'up'+'thean'+'te'='UP THE ANTE'
(Other definitions for up the ante that I've seen before include "To increase demands" , "Lift stakes" , "Demand more" , "increase danger?" , "Raise the stakes in poker game" .)