[File : ConjCharLy.dvi] Conjectures on character degrees for the simple Lyons group Authors' names: Masato Sawabe and Katsuhiro Uno Department of Mathematics,Kumamoto University, Kumamoto,860-8555 Japan Department of Mathematics, Osaka University, Toyonaka, Osaka, 560-0043 Japan A short abstract of the paper: We prove an alternating sum version of Isaacs-Navarro conjecture, which treats radical $p$-chains and characters of any defect, for the simple Lyons group. Current status: a preprint