  We observe that a function on a group equipped with a bi-invariant word
metric is Lipschitz if and only if it is a partial quasimorphism bounded on the
generating set. We also show that an undistorted element is always detected by
an antisymmetric homogeneous partial quasimorphisms. We provide a general
homogenisation procedure for Lipschitz functions and relate partial
quasimorphisms on a group to ones on its asymptotic cones.
