An anode for a lithium battery, comprising multiple porous graphene particulates, wherein at least one of the particulates comprises multiple pores (total volume Vpp), pore walls, and primary particles of an anode active material (total volume Va), disposed in the pores, wherein (a) the pore walls contain a graphene material; (b) the primary particles are in an amount from 0.5% to 95% by weight based on the total particulate weight; (c) the particulate is embraced or encapsulated by a thin encapsulating layer of electrically conducting material having a thickness from 1 nm to 10 μm, an electric conductivity from 10−6 S/cm to 20,000 S/cm and a lithium ion conductivity from 10−8 S/cm to 5×10−2 S/cm; and (d) the volume ratio Vpp/Va is from 1.3/1.0 to 5.0/1.0.