Based on my last experience at LIS I'll give best estimates:
- from gate to passport control, probably a 15min walk
- then another 15-30 minutes in line at passport control
- once out of security, uber pick up or subway is just outside.

Uber ride into downtown, probably 25-30min, depending on traffic.
Subway into the downtown area will require one transfer, total travel time from door to door about 35 minutes if everything goes well.
If you know where to go for lunch then, figure about 90 min for that.

Then hop back on subway with one transfer to airport - 35min.

If youre already in the EU and flying within then it may be easier to just whisk to the gate. (I can't speak to how fast this part will be for you)

4.45hr - may be do-able, but really not that enjoyable if you're on a countdown timer.
LIS is a wonderful city that should really be enjoyed at a leisure pace - you wont see that much to be honest and whatever you do see will be terribly rushed.
My advice - stay at the airport and lounge it - if you really want to see LIS, build in a real stopover on the way back or save for another trip.
Any snafu will ruin your trip and may unfairly kill your opinion of LIS.
But carefully planned and with a lot of good luck, certainly possible in 4.45hrs.