A 2-distance list k-coloring of a graph is a proper coloring of the vertices where each vertex has a list of at least k available colors and vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance list (Δ+3)-coloring for graphs with maximum average degree less than $\frac{8}{3}$ and maximum degree Δ≥4 as well as graphs with maximum average degree less than $\frac{14}{5}$ and maximum degree Δ≥6.