Hello Steven,
several large clients of mine have particularly licensed LAStools for this very capability. The software excels in the AWS cloud with ease of operation and extreme scalability. A common scenario is renting 100 machines with 8 cores each, installing LAStools on all of them, processing several thousand square kilometer of LiDAR using tile-based and multi-core processing on all machines in parallel. and then saving the results, uninstalling the machines, and giving them back as soon as possible. To adapt LAStools for particular workflows it is also possible to "hire" me to come on-site and perform the necessary customization to your workflow and do some I/O optimization. Often folks will combine LAStools with raster processing software such as GDAL, their own in-house solutions, or other script-able software. Also OpenTopography has been using scripted LAStools driven by a server handling Web requests since 2011.
Would be nice to have someone chime in who is running LAStools scripted in the cloud, on a server, and in particular via AWS with some actual details. I have been meaning to write a blog article on the topic of running LAStools on a server / in the cloud / and else. Overall it has been my experience that my commercial clients rend to be a little hesitant to talk about how they use LAStools given the amount of work and know how that goes into designing efficient workflows... (-;
Regards from Costa Rica,
Martin @rapidlasso