In personal names of the IOM by JJ Kneen he states that Looney is a variation of Lewney which apparently derives from Mac Lawney -1504, Lownye, MacLoney, Luney etc.
Goidelic - Mac Giolla Dhomhnaigh, 'son of Giolla Dhomhnaigh'(the Lord's servant). 
 However, I did read some time ago (and I can't remember where) that the O'Looneys were Irish chieftains. This seems to be confirmed by a section on surnames in my Readers Digest Great Encyclopaedic Dictionary where it states
Looney (Irish, Manx) O'Looney From Irish O Luanaigh 'descendant of Luanach (warrior) or O Luinigh 'descendant of Luineach (armed).
So you make your choice!  No way of knowing the exact origins of latterday Looneys.