In the paper we present measurements of the in-plane λab(T) (H ‖ c) and out-of-plane λ⊥(T) (H⊥c) penetration depths in La2−x Sr x Cu1-yZnyO4 for x = 0.08, 0.1, 0.125, 0.15, and 0.2, and for y = 0, 0.005, 0.01, and 0.02. The penetration depth was obtained from ac susceptibility measurements of powdered samples, immersed in wax and magnetically oriented in a static magnetic field of 10 T. For unsubstituted, underdoped samples (x < 0.15) penetration depth varies linearly with temperature for low temperature region. For the samples from the overdoped region (x > 0.15) the measured points can be fitted by the exponential function of temperature. Our results support the view that for underdoped samples we are dealing with Bose-Einstein condensation while for overdoped ones the superconductivity is BCS-like. Extrapolated to T = 0, penetration depth values may be described by the quadratic function of strontium concentration similarly as the T c(x) dependence. For zinc-doped, underdoped La1.85Sr0.15Cu1−yZnyO4 the temperature dependences of penetration depths can be described by power laws, but with exponents n varying linearly with substituent content. These exponents n increase at a rate of about 2.5 per at% of zinc substitution. We found that the penetration- depth anisotropy is dependent on substituent content in La1.85Sr0.15Cu1-y,Zny04, decreasing to a minimum at x ≃ 0.015 and increasing for higher substitutions and can be described by a quadratic function. Our results strongly suggest that both the effective mass and the density of charge carriers must be taken into account in theories describing high-temperature superconductivity.