The missing mass spectroscopy of the $^{7}_{Lambda}$He hypernucleus was performed, using the $^{7}$Li$(e,e^{prime}K^{+})^{7}_{Lambda}$He reaction at the Thomas Jefferson National Accelerator Facility Hall C. The $Lambda$ binding energy of the ground state (1/2$^{+}$) was determined with a smaller error than that of the previous measurement, being $B_{Lambda}$ = 5.55 $pm$ 0.10(stat.) $pm$ 0.11(sys.) MeV. The experiment also provided new insight into charge symmetry breaking in p-shell hypernuclear systems. Finally, a peak at $B_{Lambda}$ = 3.65 $pm$ 0.20(stat.) $pm$ 0.11(sys.) MeV was observed and assigned as a mixture of 3/2$^{+}$ and 5/2$^{+}$ states, confirming the gluelike behavior of $Lambda$, which makes an unstable state in $^{6}$He stable against neutron emission.