If the libor rate stays the same -which implies that also the eurodollar future quoted price remains the same- (ie: jun '22 prices is trading at 99.8, and it expires at 99.8), does the investor that purchased this contract make money for buying this contract?
No, an investor that buys or sells the contract at 99.80 will make zero money if the contract expires at that price. (Not sure what you mean by lending. )Also note that investors may make or lose money prior to maturity if the price is moving , but in the end they will end up flat.
If we assume that this investor does not care for the possibly different exchange rates prevailing at the expiration day in comparison with the day he entered the futures contract then no.
EDIT:: I am talking about exchange rates because maybe he had to convert euros to dollars to make this transaction and after expiration convert dollars to euros back again which can result in profit or loss.