  Lapid and Mao formulated a conjecture on an explicit formula of Whittaker
Fourier coefficients of automorphic forms on quasi-split classical groups and
metaplectic groups as an analogue of Ichino-Ikeda conjecture. They also showed
that this conjecture is reduced to a certain local identity in the case of
unitary groups. In this paper, we study even unitary group case. Indeed, we
prove this local identity over $p$-adic fields. Further, we prove an
equivalence between this local identity and a refined formal degree conjecture
over any local field of characteristic zero. As a consequence, we prove a
refined formal degree conjecture over $p$-adic fields and we get an explicit
formula of Whittaker Fourier coefficients under certain assumptions.
