  We derive the BPS equations satisfied by lump solitons in $(2+1)$-dimensional
sigma models with toric 8-dimensional hyper-K\"ahler (${HK}_8$) target spaces
and check they preserve 1/2 of the supersymmetry. We show how these solitons
are realised in M theory as M2-branes wrapping holomorphic 2-cycles in the
$\bE^{1,2}\times {HK}_8$ background. Using the $\kappa$-symmetry of a probe
M2-brane in this background we determine the supersymmetry they preserve, and
note that there is a discrepancy in the fraction of supersymmetry preserved by
these solitons as viewed from the low energy effective sigma model description
of the M2-brane dynamics or the full M theory. Toric ${HK}_8$ manifolds are
dual to a Hanany-Witten setup of D3-branes suspended between 5-branes. In this
picture the lumps correspond to vortices of the three dimensional ${\mathcal
N}=3$ or ${\mathcal N}=4$ theory.
