We present the results of measurements of the penetration depth anisotropy in pulverized, ceramic La2-xSrxCuO4. The measurements were carried out for x = 0.08, 0.1, 0.125, 0.15 and 0.2. The powdered samples, immersed in wax, were magnetically oriented in a static magnetic field of 10 T. The penetration depth in the a-b plane, ab, and perpendicular to it, , were derived from alternating-current susceptibility measurements. For underdoped samples they both vary linearly with temperature (for the low-temperature region), while for the samples from the overdoped region the measured points can be fitted by an exponential function. These results support Uemura's picture (Uemura Y J 1997 Physica C 282-287 194) of crossover from Bose-Einstein condensation to a Bardeen-Cooper-Schrieffer mechanism of superconductivity. The penetration depth values extrapolated to T = 0 may be described by a quadratic function of the strontium concentration (for both ab and ). The anisotropy of the penetration depth as a function of the substitution shows a similar dependence to the critical temperature Tc(x).