  We analyze single-spin asymmetries (SSAs) in the leptoproduction of
transversely polarized $\Lambda$ hyperons within the collinear twist-3
formalism. We calculate both the distribution and fragmentation terms in two
different gauges (lightcone and Feynman) and show that the results are
identical. This is the first time that the fragmentation piece has been
analyzed for transversely polarized hadron production within the collinear
twist-3 framework. In lightcone gauge we use the same techniques that were
employed in computing the analogous piece in $p^\uparrow p\to \pi\,X$, which
has become an important part to that reaction. With this in mind, we also
verify the gauge invariance of the formulas for the transverse SSA in the
leptoproduction of pions.
