everything Lufthansa in Frankfurt is in/out of Terminal 1.
Yes, but Terminal 1 covers a large area, comprising three buildings (A/Z, B, and C) connected by a shuttle, the SkyLine. Concourses A and Z are in one building. It's pretty extensive; Concourse Z is on the top level of the building and serves out-of-Schengen destinations, like the U.S. and Canada (and Ireland). - also SE Asia. Downstairs is Concourse A, which services in-Schengen destinations, most of Europe. If you are fortunate to come into Terminal 1, you'll arrive at a gate on the Z Concourse level and proceed to a gate on the same level. No immigration (passport control) and no security.
But, there is this second building, Concourse B. Concourse B has both in- and out-of-Schengen gates, in separate areas separated by immigration. If your arrival flight from Ireland and your departure flight to the US are both in Concourse B, it will be another simple change, just different gates and probably, different floors.
I don't think the Concourse C building will be a factor. Concourse C seems to be reserved for charter flights to out-of-Schengen destinations.
But, what if your arrival gate is at an out-of-Schengen gate in the B concourse and your departure gate is in the Z concourse, or visa versa. The only way to get between the A/Z building and the B building without going out through security and coming back in again is to use the SkyLine shuttle. The SkyLine has segregated sections of the stations in both the A/Z building and the B building. The isolated, out-of-Schengen parts of the B concourse and the Z Concourse, as well as the out-of-Schengen parts of Concourse D/E, are called the "transit" zone. It is possible to move, using the SkyLine, within the "transit" zone without having to go out of security or into the in-Schengen zones.