I have transferred in FRA numerous times on LH. Yes, as a Gold Member you are allowed entrance to LH Senator & Business Lounge. FYI- The distance from UA's gates to LH European gates is a long hike! My advice, go to the Senator/Business Lounge near your gate for Rome. Just look up arrrival/departure for Rome on LH's web site and you'lll get an idea of the area the A gates are located in relation to UA's gate.
While the Senator's Lounge has better food/liquor/candies, the Business Lounge has the showers. What I normally do, when not traveling 1st class, is check in at the Senator's/Business Lounge by gate A26. They have the same entrance. I go into the Business Lounge Toilette (Toilet)/ Dusche (Shower) and sign up to take a shower. I let the attendant know, I'll be in the Senator's Lounge. When it is your time, she will come into the Senator's Lounge to get you when it is your turn. The showers come complete with soap, shampoo, shaver/cream, comb, lotion, towels and hair dryer. Be advise, this can be a long wait or very quick, depending on demand. I always leave a euro or two for the attendant. Nothing like a hot shower after a night on the plane. In FRA the showers are the same, but in MUC the Gold Members get the better shower!
I also bring on board my red eye to Europe slippers, sleepwear and a hanger. Once on the plane, I change into the sleepwear/slippers and hang my clothes up on the hanger. The flight attendant will hang up your clothes and you are comfortable during the flight. Make sure you leave enough time to change back into your clothes before the flight lands. This way my clothes don't have that "slept in look" and they are fresh for the next day. ALWAYS wear slippers into the lav's and walking around the plane. You never know what is on the floor!
FRA can be a very confusing airport for the 1st time. My advice, don't wonder through FRA after drinking all night on the plane. I wound up going through passport control 5 times! If you have any more questions, you can message me.
Pleasant Travels!
D