Do yourself a favor, replace that cheap fan with either a Fantastic Fan or a MaxxFan, both are good fans, Fantastic Fans use mostly analog controls, Maxxfans have more speed settings and use digital controls, there are many sub models, some with thermostats and motorized vent covers, some without, but all are better than that piece of junk that came with your RV.
You bought the wrong lid. They’re not uncommon, your local dealer will likely have one.