  We compute an explicit $e$-positive formula for the chromatic symmetric
function of a lollipop graph, $L_{m,n}$. From here we deduce that there exist
countably infinite distinct $e$-positive, and hence Schur-positive, bases of
the algebra of symmetric functions whose generators are chromatic symmetric
functions. Finally, we resolve 6 conjectures on the chromatic symmetric
function of a lariat graph, $L_{n+3}$.
