It looks like you have vertex snapping already enabled.
Go from edge select mode to vertex mode. Grab the vertex in question and select g then Y. (I’m assuming that Y is towards the back of the scene, and that you want the lines to be vertical instead of diagonal.). If you have to instead of using global alignment you can use face alignment, though you may find that Y is not towards the back of the screen for the face. You may need to use X instead.
Then just ctrl+click on the vertex that’s lined up the way you want, and your edge should be good.
You could also try pressing ‘g’ twice to slide the vertex along the edge, then ctrl-click on the appropriately aligned vertex.
If you would prefer not to have the edges at all you could press x then choose dissolve edges.
