  We consider a class of spectral multipliers on stratified Lie groups which
generalise the class of H\"ormander multipliers and include multipliers with an
oscillatory factor. Oscillating multipliers have been examined extensively in
the euclidean setting where sharp, endpoint $L^p$ estimates are well known. In
the Lie group setting, corresponding $L^p$ bounds for oscillating spectral
multipliers have been established by several authors but only in the open range
of exponents. In this paper we establish the endpoint $L^p(G)$ bound when $G$
is a stratified Lie group. More importantly we begin to address whether these
estimates are sharp.
