The License itself is a legal document. And it's out of scope of this forum. It's up to you and your Splunk representative (which is kinda funny since your account says "Splunk Employee" ;-)) to discuss whether or not you'd be in violation of license agreement terms and provisions in "mid-migration" (for example if you doubled your ingestion rate because you were sending data to both old and new environments, Splunk might not be happy about that; but then again if it's only for a short time, maybe it would be OK; I don't know I never dug that deep into that).
The license key/license file/however you call that, is a piece of digitally signed XML which - after you upload it - is stored on your license manager in $SPLUNK_HOME/etc/licenses and is easily transferable between hosts.
So technically - yes, you can copy the file over. Legally - it depends if you should/can do so.
In the simplest case - if you just want to move the LM to another machine while keeping all other components intact, just spin up a new LM, copy the config from the old one (adjusting the server names, certificates and IPs if necessary), point your license peers to a new LM (easy to do if you have config managed with apps, more manual work if you have the config in system/local), after a day or two retire the old LM and you're done.