An awful lot of fun means a great deal or plenty of enjoyment. It is an idiomatic expression used to describe something that is very entertaining, exciting and enjoyable.
All the stores are filled with beautiful Spring clothing right now and although I may not be able to wear them for a few months, I am having an awful lot of fun trying them on. (whatsarahknows.com)
Full of knowing nods for fans and stunningly designed, Captain America might not be perfect but it is an awful lot of fun. (rottentomatoes.com)