Try this to solve your start and end date being in the same month:

=IF([@[Start Date]]>0,IF(OR(AND([@[Start Date]]<'LookUp Table'!$B$13,[@[End Date]]>'LookUp Table'!$D$12),MONTH([@[Start Date]])=MONTH([@[End Date]])),[@[% time]],""),"")

I've just checked to make sure you have something in the start date first, then added an OR around your original formula, with a second condition to check if the month is the same in both the start and end dates.

I'm not clear about what behaviour you expect to see if the start and/or end dates are part way through the month?