There are not yet many online courses strictly focused on the lightning network. But here are a few Bitcoin courses that we recommend that provide an excellent background for understanding lightning.
Payment Channels and Lightning Network, MIT, 2018, Lectures 13 and 14, Tadge Dryja (leading expert). Great graduate-level lectures. Part of a very good bitcoin course entitled Cryptocurrency Engineering and Design. Very technical (It is a graduate-level MIT course), but interesting and relevant. Really shows the deep complexity lurking behind the Lightning Network.
Blockchain and Bitcoin Fundamentals, Udemy, $11.00. 3 hours of video instruction and a nice pdf glossary.
Introduction to Digital Currencies, University of Nicosia, Andreas Antonopoulos, MOOC on Moodle platform, Self-study with live weekly lecture/Q&A Thursdays 10-11 EST. 12 weeks, weekly quizzes and exam, superb integrated bibliography. Great practical exercises. Week 5 covers the Lightning Network. Certificate program (on a blockchain). Available as part of an MSc in Digital Currency. MOOC 13 started Jan 20, 2020.
Lightning Network 101, iCEX. A text-based short course covering basics, some basic use cases, hands-on, and 10 question quiz.
Lighting Network Explained, Bitdegree.org. Aug 2019, 3,000-word summary. A good high-level overview of how LN addresses the limitations of Bitcoin. NOT really a course
Bitcoin and Cryptocurrency Technologies, Coursera/Princeton, 18-hour, 11-week course. 2015. Four lecturers. Very well produced course. Great motivational details and google calendar integration. Early sections are quite technical but necessary. Dated but highly recommended. Videos are also available on YouTube.