The following spelling rule explains that likely is spelled likely rather than likly.

A. When the suffix ends with a consonant, keep the "e" on the main word.
B. When the suffix begins with a consonant, keep the "e" on the main word.
C. When the main word ends in "e", keep the "e" and add "ly" (I don't think this one is right myself.)
D. When the main words end in a consonant then a vowel, keep the "e" and add "ly"