Essential Matrix from line correspondences
When I think of lines in correspondence, my mind immediately goes for Pluecker representations, which are very suitable for such estimation tasks. In fact this work exists for camera pose estimation from lines and might be a good starting point:


  Přibyl, Bronislav, Pavel Zemčík, and Martin Čadík. "Camera Pose Estimation from Lines using Pl\" ucker Coordinates." arXiv preprint arXiv:1608.02824 (2016).
  (link to the project page)


As you mentioned, there are various resources, especially when your camera is calibrated (I assume this because you ask for the essential matrix). If you really like to have a quick and dirty solution, you could either use the endpoints of the line segments (if you have them) or the intersection points of the lines.

In fact this just reminded me of one nice work, which generates virtual points on cameras along the lines and uses them for pose computation:


  Line-Sweep: Cross-Ratio for Wide-Baseline Matching and 3D Reconstruction
  S. Ramalingam, M. Antunes, D. Snow, G. H. Lee, S. Pillai
  Computer Vision and Pattern Recognition (CVPR), 2015
  (link to the project page)


Let's keep here posted with updates.