From experience, OpenRailwayMap can be inaccurate. Best way (even though it's somewhat tedious) is to find a cabview video and read the speed signs the same way a real driver would. Then track their position on the map. For example by counting catenary masts from something that's easily recognizable.
i know this is an old post im finally at track laying, that OpenRailwayMap looks really good which i will mix with cab view rides. mine only issue is where can i find gradients as the only place i can find them is a TSC video on youtube which is super inaccurate according to the part of route im at
For gradient data, I would just trace the route in QGIS and get elevation from the LIDAR data that you have. Then mark places where the grade changes and calculate the percentage. Just remember that 0.1% grade is 1 meter of elevation difference for 1000 meters of distance. I even wrote a tutorial on how to make gradients. https://forums.dovetailgames.com/threads/gradient-plotting-mini-tutorial.76169/