OK, we have done our first round with a Brompton as a carry-on. Security was no issue at all. They spent more time examining the Brompton bag and my backpack than the bike. A cable coil lock on the bike was not a problem. We have not tried a U-lock yet.

The airline, Delta, however, was a problem. At the entrance to the first plane, we did not cover the bike and the agent was upset that we did not declare the bike at the check-in counter and pay the bike fee. Since the plane was about semi-boarded, he warned us that we have to do it next time and let us in. For the second leg, we put the Brompton cover on and claimed that it was a type of foldable stroller. The agent was suspicious regarding what was under the cover and exploring the possibilities of sending it off with checked luggage and putting the bike to an overhead bin. (The plane turned out to be large and it might have accommodated the bike there, but we did not want to try.) In the end, though, the agent was pressed with time and gave us the gate tag. My overall advice is to time the entrance to the plane right, not too early and not too late, so that the agent cannot spend much time on you.