  We compute the contribution from the twist-3 fragmentation function for light
hadron production in collisions between transversely and longitudinally
polarized protons, i.e., $p^\uparrow \vec{p} \to h\,X$, which can cause a
double-spin asymmetry (DSA) $A_{LT}$. This is a na\"ive T-even twist-3
observable that we analyze in collinear factorization using both Feynman gauge
and lightcone gauge as well as give a general proof of color gauge invariance.
So far only twist-3 effects in the transversely polarized proton have been
studied for $A_{LT}$ in $p^\uparrow \vec{p} \to h\,X$. However, there are
indications that the na\"ive T-odd transverse single-spin asymmetry (SSA) $A_N$
in $p^\uparrow p \to h\,X$ is dominated not by such distribution effects but
rather by a fragmentation mechanism. Therefore, one may expect similarly that
the fragmentation contribution is important for $A_{LT}$. Given possible plans
at RHIC to measure this observable, it is timely to provide a calculation of
this term.
