Before revision:  On the other hand, when the ratio is restricted to adjacent edges only, we provide a procedure that for any 2-tree yields a drawing with the ratio arbitrarily close to 4.
After revision:  On the other hand, when the ratio is restricted to adjacent edges only, we provide a procedure that for any 2-tree admits a planar straight-line drawing whose edge-length ratio is at most 4 + \varepsilon for any arbitrarily small \varepsilon > 0, hence the upper bound on the local edge-length ratio of partial 2-trees is 4.