We investigate the properties of $$\Lambda $$ hyperon in $$\Lambda $$ -hypernuclei using an effective nuclear density functional theory which is based on the low-energy effective field theory. It expands the energy density in the power of Fermi momentum, and consequently has multiple density dependence for the effective many-body interactions. Starting from the effective density functional for nucleons, we determine the parameters for the two- and many-body $$\Lambda $$ -N interactions added to the nucleon energy density functional by fitting to $$\Lambda $$ -hypernuclear data. The experimental data consist of the energy levels of a $$\Lambda $$ hyperon in the p-, and d-states as well as s-state of $$\Lambda $$ -hypernuclei in the mass range from $${}_\Lambda ^{16}\hbox {O}$$ to $${}_\Lambda ^{208}\hbox {Pb}$$ . The results turn out to properly explain the data relevant to hypernuclei owing to the effective many-body interaction apart from a few data in light hypernuclei. This hyperon functional is applied to study the $$\Lambda $$ hyperon binding energy of the neutron-rich $$^{124-136}_{\Lambda } \hbox {Sn}$$ isotopes which are under consideration for the measurement at J-PARC. Our results are shown to be insensitive to the density dependence of symmetry energy. We also examine the nuclear matter including $$\Lambda $$ hyperon. We note that the hyperon threshold density depends on the nuclear matter properties.