  Density of Lipschitz functions in Newtonian spaces based on quasi-Banach
function lattices is discussed. Newtonian spaces are first-order Sobolev-type
spaces on abstract metric measure spaces defined via (weak) upper gradients.
Our main focus lies on metric spaces with a doubling measure that support a
$p$-Poincar\'e inequality. Absolute continuity of the function lattice
quasi-norm is shown to be crucial for approximability by (locally) Lipschitz
functions. The proof of the density result uses, among others, that a suitable
maximal operator is locally weakly bounded. In particular, various sufficient
conditions for such boundedness on rearrangement-invariant spaces are
established and applied.
