Before revision:  First, we consider the version in which the corners of all input L-frames are anchored at a line with slope -1, and obtain a polynomial-time (2+\epsilon)-approximation . Furthermore, we obtain a PTAS in case all the input L-frames are anchored at the diagonalfrom one side.
After revision:  First, we consider the version in which the corners of all input L-frames are anchored at a line with slope -1, and obtain a polynomial-time (2+\epsilon)-approximation for the problem with "diagonal-anchored" L-frames. On the other hand, we show that the problem is APX-hard in case the input L-frames are anchored at the diagonalfrom one side.