  BPS lumps in ${\cal N}=2$ SUSY nonlinear sigma models on hyper-\kahler
manifolds in four dimensions are studied. We present new lump solutions with
various kinds of topological charges. New BPS equations and a new BPS bound,
expressed by the three complex structures on hyper-\kahler manifolds, are
found. We show that any states satisfying these BPS equations preserve 1/8
(1/4) SUSY of ${\cal N}=2$ SUSY nonlinear sigma models with (without) a
potential term. These BPS states include non-parallel multi-(Q-)lumps.
