4 hours is plenty of time.
A non-Schengen to non-Schengen connection requires security, however if you are arriving with LOT, you are in Schengen. So which is it?
I start at Tokyo, but you're right, the last leg will be WAW to ATH so indeed Shengen. My full route is NRT-WAW-ATH-TLV (don't ask why..), where the first two legs are with LOT, and the last with ElAl.
I'm trying to figure out how much hassle checking in luggage would add to my route. I was assuming I don't need to pick up luggage and check it back in at WAW, but perhaps I do?