I did my first proper Deadlifts session yesterday with reasonable weight.
Silly question but is it normal to have quite a sore lower back the day after? My traps are incredibly sore as well.
It's normal if you don't keep the weight of your lower back, yes.

Also, if it's the first time, your erectors are probably asking you "what the hell did you just do?" as well...
Your traps are sore because they were holding your shoulders back. Good work.
