When you have the point every 50m along your line, how many points are you wanting to find? do you only want to the the one closest point, or are you looking for all points within XXm?

Using a PointcloudCoercer you'll be able to extract the individual points from the point cloud and use PointOnArea, SpatialRelator, SpatialFilter (theres a few spatial transformers you could use) to filter those points. Then using a PointCloudCombiner you can convert your filtered points back into a pointcloud and write them out to a LAS