(A) Emitting an particle would reduce the atomic mass by units and the atomic number by units. Therefore, this is not correct.
(B) Emitting an electron only would give the atom a net positive charge. Therefore, this is not correct.
(C) Emitting a neutron only would reduce the atomic mass by unit and keep the atomic number unchanged. Therefore, this is not correct.
(D) Emitting a positron only would give the atom a net negative charge.
(E) Electron capture by the nucleus means that a proton in the nucleus combines with an electron in the atom to form a proton. The neutrino (which is actually an electron neutrino) is emitted in order to conserve electron number. This is consistent with the end product of lithium-. Therefore, this answer is correct.