While true, this phrase considerably predates the US Revolution. The term probably comes from the "Low Country Wars" between the Catholic Spanish Empire and the Protestant Rebels in the Netherlands in the 1500s. In Dutch, "Verloren Hoop" is 'lost troops', and in usage means a military company sent or ordered to remain where their personal survival was secondary to the task ordered.
England had been deeply involved in this area with the wool trade and under the latter Tudors and early Stuart monarchs, decided to aid this fellow Protestant country as another method to fight Spain. With the English troops fighting alongside the 'Dutch Rebels', the Dutch term of 'verloren hoop' morphed via homonym transfer into English as 'forlorn hope'.
FYI: This revolt / war lasted from the mid-1500s to 1648 with the Peace of Westphalia which divided the area into Holland (Protestant) and Brussels (Roman Catholic). Shortly thereafter came the Anglo-Dutch trade & maritime wars that were then followed by the anti-French 'War of the League of Augsburg' and the 'War of the Spanish Succession'. Lots of fighting because absolutism gives religious and autocrats excuses to send the peasants out to fight!
Bernard Cornwell’s Sharpe series chronicles a British soldier in the Napoleonic Wars. In those tales the Forlorn Hope were the volunteers who were the first to assault a fortress. When he was feeling particularly low, Sharpe volunteered for one and, of course, survived.
One of the groups that semi-successfully broke out of the Truckee Lake Donner Party camp called themselves the “Forlorn Hope”. It seems that ordinary folk were somewhat better educated than we are today.