Competition from AMEX isn't going to cause UA to improve it's lounges; the UCs are already overcrowded and I'm sure UA is happy to have AMEX pick up some of the overflow.
The "competitive pressure" that would cause UA to upgrade its lounges is other carriers (particularly DL and AA) taking its high value flyers away. That's the impetus for the Polaris lounges . . . attract and retain the international paid J traffic with a better lounge product. (So far of course execution has, in typical UA fashion, been a total fail.)