T3-T3 connection at London Heathrow

I'll be connecting from LYS at T3 to another ongoing flight to RDU also at T3. Since both are in the same terminal, do I need to follow the signs for Flight Connections and go through security? Or do I just get dumped into the terminal and find my way around? I am coming from France so do I need to go through immigration?

Just follow the signs for Flight Connections Terminal 3. You will clear security to get into the main departures lounge where the shops and restaurants are, but no other formalities are needed (on the assumption that your bags will be through-checked to RDU, which they should be if you're travelling on one ticket).