We numerically obtain a class of soliton solutions for Einstein gravity in (n+1) dimensions coupled to massive abelian gauge fields and with a negative cosmological constant with Lifshitz asymptotic behaviour. 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=2; moreover, in all cases, a single magic value is obtained for essentially every 12 sufficiently.