  We investigate the fishtail effect, critical current density ($J_c$) and
vortex dynamics in LiFeAs single crystals. The sample exhibits a second peak
(SP) in the magnetization loop only with the field $||$ c-axis. We calculate a
reasonably high $J_c$, however, values are lower than in 'Ba-122' and
'1111'-type FeAs-compounds. Magnetic relaxation data imply a strong pinning
which appears not to be due to conventional defects. Instead, its behavior is
similar to that of the triplet superconductor Sr$_2$RuO$_4$. Our data suggest
that the origin of the SP may be related to a vortex lattice phase transition.
We have constructed the vortex phase diagram for LiFeAs on the
field-temperature plane.
