The surface impedance at 10 GHz was measured systematically in single-
crystal La2-xSrxCuO4 for carrier concentrations 0.09 less-than-or-equa
l-to x less-than-or-equal-to 0.19, from which the penetration depth la
mbda was determined. The anisotropy and the dependences on x and tempe
rature T of lambda are extensively studied for the first time. The ani
sotropy of lambda(T = 0) decreases with increasing x, and still remain
s larger than 10 for x = 0.19. The out-of-plane penetration depth (lam
bda(ab)) has a different temperature dependence from the in-plane one
(lambda(ab)). These results suggest that the electrodynamic properties
in the superconducting state along the c axis can be explained by a J
osephson-coupled layer model.