  The structure of neutron-rich $\Lambda$ hypernucleus, $^7_{\Lambda}$He is
studied within the framework of an $\alpha +\Lambda +n+n$ four-body cluster
model. We predict second $3/2^+$ and $5/2^+$ states, corresponding to a $0s$
$\Lambda$ coupled to the second $2^+$ state of $^6$He, as narrow resonant
states with widths $\Gamma \sim 1$ MeV to be at 0.03 MeV and 0.07 MeV respect
to the $\alpha +\Lambda +n+n$ threshold. From an estimation of the differential
cross section for the $^7{\rm Li} (\gamma,K^+) ^7_{\Lambda}$He reaction, there
is a possibility to observe these state at JLab in the future. We also
calculate the second $2^+$ state of $^6$He as resonant state within the
framework of an $\alpha +n+n$ three-body cluster model. Our result is $2.81$
MeV with $\Gamma =$4.63 MeV with respect to the $\alpha +n+n$ threshold. This
energy position is $\sim 1$ MeV higher, and with a much broader decay width,
than the recent SPIRAL data. It is suggested that an experiment at JLab to
search for the second $3/2^+$ and $5/2^+$ states of $^7_{\Lambda}$He would
provide an opportunity to confirm the second $2^+$ state of the core nucleus
$^6$He.
