Can Galileons solve the muon problem?

The leptonic bound states positronium and muonium are used to constrain galileon contributions to the Lamb shift of muonic hydrogen. Through the application of a variety of bounds on lepton compositeness, it is shown that either the assumption of equating the charge radius of a particle with its galileon scale radius is incompatible with experiments or the scale of galileons must be $M>1.33$ GeV, too large to solve the muon problem. The possibility of stronger constraints in the future from true muonium are discussed.