For an abelian group $H$ acting on the set $[\ell]$, an $(H,\ell)$-lift of a graph $G_0$ is a graph obtained by replacing each vertex by $\ell$ copies, and each edge by a matching corresponding to the action of an element of $H$. In this work, we show the following explicit constructions of expanders obtained via abelian lifts. For every (transitive) abelian group $H \leqslant \text{Sym}(\ell)$, constant degree $d \ge 3$ and $ε> 0$, we construct explicit $d$-regular expander graphs $G$ obtained from an $(H,\ell)$-lift of a (suitable) base $n$-vertex expander $G_0$ with the following parameters: (i) $λ(G) \le 2\sqrt{d-1} + ε$, for any lift size $\ell \le 2^{n^δ}$ where $δ=δ(d,ε)$, (ii) $λ(G) \le ε\cdot d$, for any lift size $\ell \le 2^{n^{δ_0}}$ for a fixed $δ_0 > 0$, when $d \ge d_0(ε)$, or (iii) $λ(G) \le \widetilde{O}(\sqrt{d})$, for lift size ``exactly'' $\ell = 2^{Θ(n)}$. As corollaries, we obtain explicit quantum lifted product codes of Panteleev and Kalachev of almost linear distance (and also in a wide range of parameters) and explicit classical quasi-cyclic LDPC codes with wide range of circulant sizes. Items $(i)$ and $(ii)$ above are obtained by extending the techniques of Mohanty, O'Donnell and Paredes [STOC 2020] for $2$-lifts to much larger abelian lift sizes (as a byproduct simplifying their construction). This is done by providing a new encoding of special walks arising in the trace power method, carefully "compressing'" depth-first search traversals. Result $(iii)$ is via a simpler proof of Agarwal et al. [SIAM J. Discrete Math 2019] at the expense of polylog factors in the expansion.