Female musical artists such as Madonna, Lady Gaga and M.I.A. understand that to truly compete in a male-dominated entertainment business, one cannot be afraid to push boundaries. Whether utilizing outlandish clothing and costumes, outspoken rhetoric or musical theatricality, each one has risen in the ranks of their respective genres with increasing success. While the prospect of a recording collaboration or live performance has little likelihood between these three, particularly following M.I.A.'s numerous insults towards Gaga, Washington-based DJ Lil'e is trying her best to create the best hypothetical gig she can with a dance-music mash-up. Following her sold-out show at the 9:30 Club, DJ Lil'e is scheduled to bring her Lady Gaga vs. Madonna vs. M.I.A. party to the National on Friday, Dec. 3, at 8 p.m. $10.