I think this is about a couple who have broken up and have both found someone else. But he doesn't seem to like being apart from her - "It doesn't feel right holding someone else's hand".
"Together on phone lines, living at two opposite ends" - Means that they're not living together.
I think the next couple of lines mean that she has split up with him for someone else who is 'better than him'.
"These laces are untied, but my feet are still walking away" I think this means that there are still things that need to be said but he's just leaving it out. The next bit is him thinking back to her breaking up with him, and how she suggested they can still be friends. "How can you take all these days and throw them away?" He wonders how she could just throw away their time together and move on like that.