Why would "Modernising their databases" require something like Lab computers to be connected to the Internet -- I just don't see what the connection is here -- these machines can be run "Stand alone" or even as Virtual Machines.
I would surmise you've got somebody in I.T services telling you big "Porkies" (or trying to flog you something). - Outsourced Contractors / services perhaps !!!
What on earth would the Internet have to do with some Machine tool equipment designed before the Internet was even THOUGHT OF !!!. Honestly some I.T guys seem to get away with Blue Murder. I must admit though I had a huge laugh when I read your post about "Modernising their Databases". !! A database surely only has DATA in it --if they need to audit and validate computer hardware and software there are all sorts of ways of doing it - you don't need to have an Internet connection -- and with the case of these legacy systems there shouldn't be any more licensing problems either.
I'll do your "Database update" for a lot cheaper than your current supplier and a lot quicker too if you like.