Woo, hold on a minute. You do realize swaping your car to run an Integra automatic transmission is going to involve converting your entire in-car harness to an Integra unit (including everything behind the dash). Someone on this board a while back (a good few years, I don't remember his screen name and don't think he posts anymore) did this swap and he said he'd never do it again even though he did get it to work (his girlfriend wouldn't learn to drive a stick). I believe the automatic's controls are in a seperate ECU and harness from the main engine ECU and the only way to install one in a Civic is to convert everything to the Integra units. To be perfectly honest with you, if you want an automatic Integra engine, go buy an automatic Integra, you'll save having your car down for a few weeks/months while you do all the wiring and you still have hair on your head.

If your car is already an automatic LX and you want to keep it, your best bet is to swap one of the SOHC VTEC engines if you really want a new engine. I'm not sure what year your car is, but the D16Z6 is the '92-'95 SOHC VTEC and the D16Y8 is the '96-'00. Your best bet would be to find a junkyard low milage EX version and swap everything over. I've never done an automatic swap but D-series to D-series shouldn't be that diffucult. Honestly, if your seriously looking for a performance upgrade, and I'm not saying this as a smart arse comment but just cold honest reality, your not going to get very far with an automatic transmission. You'll notice Honda's performance engines (DOHC VTEC B-series basically) were never available with an automatic. Automatics are also limited and in how much abuse they can take from an upgraded engine and the aftermarket support for them is very limited.