Welcome to the forums!
You are correct on your gorgeous couple's genders, Lulu is a female and Romeo is a male.
Has Lulu been constantly bullying Romeo? Sometimes there are light bickerings between budgies especially as they are getting ready to sleep for the night, they can also argue over food. To avoid the bickerings over food or a favourite toy, it's always best to have twos of everything, two food dishes, two separate pieces of vegetables for each of them, two toys of the same characteristics, etc.
If Lulu has dented Romeo's beak, then that falls under the more vicious fighting category and for your boy's safety it would be best to separate him from Lulu.
Since her cere is now dark brown it really does mean she is in breeding condition and she can in fact get more moody during this time. Just do not give her anything that she could use as a nest, sometimes the behaviour can escalate to worse when a nest or hiding spot is made available to them.
Eventually her cere will revert to the creamy white colour and she will be out of breeding condition.
Keep a close eye on them and if you see bad fighting then do separate each budgie into it's own cage. You can move your Lulu into a different cage and by doing so you have a good chance of her going out of breeding condition.
Your Romeo's beak will heal with time, you don't need to worry.