It depends on the situation. Do you plan to pay the full amount owed, including all the expenses incurred on the day you paid? If so, when? The most important thing is that you shouldn't start to worry really until the days and hours when you are asked to leave. In almost all cases, this appears to be three days from the date of notification (if the date is different, it is not the date you received the notice). However, this is still a very serious situation and should not be underestimated.

My notice says this is "unconditional" but offers another option. 

Usually, unconditional notifications are bad news. This means that even if you pay the money you owe, you will not have a second chance, you must abide by the requirements. Confusingly, a notice of moving out seems to always follow directly, which seems to be contradictory, and it provides an opportunity to solve the problem. How can it claim to be absolute when something offers a possible opportunity? Ok, in fact, you still have a choice. According to my experience, frankly, the word "unconditional" was abused in these notices.

I want to talk to the staff, but they are closed!

It's not uncommon at all, because for this reason, it's worth putting it here. My notice was not discovered until one day after the front hall of my apartment building was closed. If they are open, I will find that all my fears and panic are for no reason. Please see the next question.

Do I need to find a lawyer?

Not exactly yet. If you have just received a notice to move out, and the front hall of your apartment is still open, stop reading, go talk to them now. They should be your first person to consult.