  Given a tropical line $L$ and a smooth tropical surface $X$, we look at the
position of $L$ on $X$. We introduce its primal and dual motif which are
respectively a decorated graph and a subcomplex of the dual triangulation of
$X$. They encode the combinatorial position of $L$ on $X$. We classify all
possible motifs of tropical lines on general smooth tropical surfaces. This
classification allows to give an upper bound for the number of tropical lines
on a general smooth tropical surface with a given subdivision. We focus in
particular on surfaces of degree three. As a concrete example, we look at
tropical cubic surfaces dual to a fixed honeycomb triangulation, showing that a
general surface contains exactly $27$ tropical lines.
