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Paranoid = yes. Lock = no (faff to get it off in time when I want to get off, & guards don’t like it much).
I try to sit at one of the seats right near the rack, or stand with it in the hallway if it’s busy. Fortunate it’s only 35 mins for me so standings is ok most of the time if I can’t get a seat.
Saying that, never had/see a problem (and there’s lots of Bromptons leaving Paddington…)
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when I did vauxhall to feltham, I'd usually stand with it at my feet in busy times, when I couldn't get a seat, or sit with it beside me, when i could get a seat. Never really left it any further than my hand could reach it. Never took a lock as it (to my mind) defeats the purpose of having a brompton, since you can take it inside with you.
Folks who commute with their Brompton on the train: do you ever get paranoid leaving it on the luggage rack by the doors? Do you use a little lock or anything?