  In this paper, we obtain inequalities for some integrals involving the
modified Lommel function of the first kind $t_{\mu,\nu}(x)$. In most cases,
these inequalities are tight in certain limits. We also deduce a tight double
inequality, involving the modified Lommel function $t_{\mu,\nu}(x)$, for a
generalized hypergeometric function. The inequalities obtained in this paper
generalise recent bounds for integrals involving the modified Struve function
of the first kind.
