How can I host LEM on AWS?
You basically need to grab the disk image from the LEM appliance and upload it to AWS, that should work.
To add, an OVA is really just a .tar file, so if you rename the LEM OVA to a .tar and untar (or, if you have better tar tools that let you untar even with out the .tar extension you might not even have to rename) you should get the vmdk. OR, you could use the Hyper-V VHD, too, I think AWS will pull VHDs directly.
Step 4: Importing Your VM into Amazon EC2 - Amazon Elastic Compute Cloud
That said, AWS isn't listed as a supported platform for LEM, so any uncertainties in operating LEM brought about by the platform (performance, configuration, etc) will probably not be well received by SolarWinds. You can check with them on current status.