It is not so much the storyline, but the music that overlaps. The music "written" in the storyline of "The liar and his lover" is even played by street musicians in "I am not a robot". It is probably the only overlapping song, since TLAHL is a music focussed drama and IANAR only has background music, but maybe it is the production, too, I just think, if you liked the one, you might like the other, too. Give it a try.
