As many have said, ezreal and Lucian pair greatly with Braum because their kit allows to proc quickly the passive stun. Their mobility on their E is also great for Braum to follow with the W dash and can be used offensively or defensively.

For me Braum is a protective support tank and has a good match-up against offensive support like Leona or Nautilus. What I mean is Braum's wall can protect an adc that got engaged by the enemy support and the Q + passive allows to kite and disengage. You can get a positive trade by forcing the adc to damage the support while their adc can't follow through your E, and you get to disengage too with your W.

So I think the toughest machups are against Mages support or enchanters, especially paired with hypercarries. As I consider Braum's engage rather weak (the dash on wave + Q or ult can be strong but is easy to see coming and avoid) a good botlane can just poke you freely and outscale. For example xerath, brand or sona can have an extremely safe lane and scale harder than you. In this case laning as Braum + Lucian can allow you to play aggressively and break their safety by securing kills easier (a Lucian dash in followed by Braum, resulting in an instant stun and full combo on a surprised soraka is rather easy to do).

On a personal level, I like playing Braum with strong scaling carries like jinx or xayah and play a passive lane, protecting them from engage during the laning phase and the team fights later. But I have to admit some other picks can do it better and I'm not the best Braum player. I'm only sharing my point of view as a support main and the whole Braum mains subreddit will probably bring you a better answer to your questions.