I thought that since the airlines are both in terminal 1 that I might be able to make it.
You might, but are you willing to buy a new ticket at an inflated price if your Lufthansa flight is delayed and you miss your connection. On one ticket, the airline is obligated to get you to your final destination even if your first flight is delayed. On two separate tickets, United is under no obligation to get you home if your inbound Lufthansa flight is delayed. While it is technically possible that Lufthansa would through-check your bags, many airlines refuse to do this on two separate tickets. Check in with United (mainly for your luggage since you can check in online) closes 60 minutes before departure for international flights. If Lufthansa does not through check your bag, that leaves you only 50 minutes to get off the plane, get to the baggage area and wait for your bag, and get through the baggage drop for United. It is not a risk I would be willing to take as I would not want to risk paying several thousand dollars for a new ticket.
Have you looked into what it would cost to change your United ticket to depart from Rome rather than Frankfurt?