> So the struts (plus supporting structure) are lighter than the legs? Why is that?
Besides the other answers you've received, the lugs hold the booster from (near) the top. This means that the body of the booster is in tension during and after landing. Legs, on the other hand, support the landing load and weight after loading in compression. The booster is basically a thin-shelled tube, which is limited in compression strength (for a given wall thickness) by buckling; in tension, the strength approaches the strength of the material, so less additional reinforcement is needed in the structure to support landing loads.
Besides the other answers you've received, the lugs hold the booster from (near) the top. This means that the body of the booster is in tension during and after landing. Legs, on the other hand, support the landing load and weight after loading in compression. The booster is basically a thin-shelled tube, which is limited in compression strength (for a given wall thickness) by buckling; in tension, the strength approaches the strength of the material, so less additional reinforcement is needed in the structure to support landing loads.