I've just gotten to the Citadel and met Elder Lyons. He gives me the permission to learn power armour, but there's no dialog option for permission to trade. I've made sure all dialog options are greyed-out, and even reloaded the game and spoken to him several times. Still no option to trade.

I don't use any mods that alter characters or dialog. I only use DK Bullet Time, Fellout Brighter Nights, Weapon Modkits, and DarNified UI.

Did you talk to the quartermaster first?

I believe she has to turn you down before you can ask Lyons about trading.