I think you’ve got the name wrong. Either that or you are talking about a program that I’ve never heard of.
“LAME” (the name is just one word) is an MP3 encoding library. It’s not a “recorder”.
Unfortunately, Apple have just made it harder to run applications that don’t come from the Apple Store.
Mac computers have a security system called “Gatekeeper” that prevents “unknown” software from working (intended to stop malware from damaging the system).
Unless your students are very tech-savvy, you may need to ask your IT support to help with this.
Firstly, you need to tell Gatekeeper to allow the file to be installed, but even then Sierra may “quarantine” the file, so you may then need to use the command described in this post: Help with Plugins - macOS Sierra - #28 by icprg