The universal adjacency matrix $U$ of a graph $Γ$, with adjacency matrix $A$, is a linear combination of $A$, the diagonal matrix $D$ of vertex degrees, the identity matrix $I$, and the all-1 matrix $J$ with real coefficients, that is, $U=c_1 A+c_2 D+c_3 I+ c_4 J$, with $c_i\in {\mathbb R}$ and $c_1\neq 0$. Thus, as particular cases, $U$ may be the adjacency matrix, the Laplacian, the signless Laplacian, and the Seidel matrix. In this note, we show that basically the same method introduced before by the authors can be applied for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).