We numerically obtain a class of soliton solutions for Einstein gravity in (n þ 1) dimensions coupled to massive Abelian gauge fields and with a negative cosmological constant with Lifshitz asymptotic behavior. We find that for all n ! 3, a discrete set of magic values for the charge density at the origin (guaranteeing an asymptotically Lifshitz geometry) exists when the critical exponent associated with the Lifshitz scaling is z ¼ 2; moreover, in all cases, a single magic value is obtained for essentially every 1 < z < 2, yet none when z > 2 sufficiently.