parital answers
Is transfer at LIS and OPO relatively painless?
I suspect your mileage may vary. I had a sixty minute wait to get through immigration as a US passport holder. Very frustrating. No premium line. They were calling people with close connections to the front of the line.
Is there priority security lane for TAP at EWR and LIS?
I imagine there is at EWR (there was at BOS, even though the JetBlue employee tried to tell me the line wasn't for TAP, there was a sign indicating it was for TAP business).
In Lisbon I did not see a priority line.
I didn't check any luggage so cannot confirm whether you need to reclaim or not, but I believe the security line for transfers was before the baggage belts so imagine things get checked through.