Chemistry - Comparing ionic character of group 1 elements

Well, the second source is certainly more wrong. There is a major difference between ionic character of a bond and the stability (lattice energy) of an ionic lattice. $\ce{LiH}$ is certainly more covalent than $\ce{CsH}$ (meaning $\ce{CsH}$ is more ionic), which can be justified simply by comparing charge densities on $\ce{Li}$, which is very high and draws electron density from the $\ce{H}$ atom, forming a more covalent bond.