Even if it were possible (which looks like it's not), the CX lounge at T4 is probably not worth the possible extra effort to access if your onward flight is T1-T3. The lounge reminds me of The Deck without the shower facilities.

Just my opinion, though. Go to the city if you don't fancy staying in the airport complex or just make do with the OW lounges in T1-T3 if you're not keen to venture out.