  The absence of nesting between electron and hole-pockets in LiFeAs with $T_c
= 18$K attracts great attention, as an important hint to understand the pairing
mechanism of Fe-based superconductors. Here, we study the five-orbital model of
LiFeAs based on the recently-developed orbital-spin fluctuation theories. It is
found that the experimentally observed gap structure of LiFeAs, which is a
"fingerprint" of the pairing mechanism, is quantitatively reproduced in terms
of the orbital-fluctuation-mediated $s_{++}$-wave state. Especially, the
largest gap observed on the small two hole-pockets composed of ($d_{xz},
d_{yz}$) orbitals can be explained, and this is a hallmark of the
orbital-fluctuation-mediated superconductivity. The $s_{++}$-wave gap structure
becomes more anisotropic in the presence of weak spin fluctuations. As the spin
fluctuations increase, we obtain the "hole-$s_\pm$-wave state", in which only
the gap of the large hole-pocket made of $d_{xy}$-orbital is sign-reversed, due
to the cooperation of orbital and spin fluctuations. %out of the five pockets.
This gap structure with "sign-reversal between hole-pockets" is similar to that
recently reported in (Ba,K)Fe$_2$As$_2$.
