D2 is my desired start date, and E2 is my desired finish date. Column
CA is Jan 1-31, so I am trying to see if my start date or finish date
is in January, I then want to drag the same formula to look in
February, March, etc

Here's one way, but it doesn't use a lookup.

In a column of your choice, put this in row 1 and copy down to row 12:
=TEXT(DATE(2000,ROW(),1),"Mmmm")&
" "&
IF(MONTH($D$2)=ROW(),"Start ","")&
IF(MONTH($E$2)=ROW(),"End ","")

Modify to suit.