Unfortunately, it's not possible. You can only access the airside lounges as a transit passenger (in which case when you transfer, you're stuck airside and there's no "out").
You'll have to head directly to immigration and exit to landside. In the AREX train terminal building, there is luggage storage service. Also, when you return to ICN airport - there are FREE showers in the 4th Floor Rest & Relax area you can use. Just show your arriving and your departing boarding pass for free use....if you just show departing one only, it's 3,000W for "originating passengers." I have used these showers before and they are just as nice as any lounge shower.
And FYI you will have around 8:30-12:30ish in Seoul. Take the train into the city to avoid any traffic surprises. Visit the Gyeongbokgung Palace, Gwangjang Market, etc. I actually never do this BUT on my website I have a section of tourist tips....since everyone always asks about one day tours/layovers
https://therealseoul.com/2018/06/15/...port-transfer/