Can I take a train from Gare Saint-Lazare to Brussels?
Trains mainly depart from the Paris Nord stations (which is one station away on RER E from Saint-Lazare, or a 15-20 minute ride by metro or bus) and from Charles de Gaulle Airport. Buses mainly depart from Bercy, which is close to Gare de Lyon (10-15 minutes by metro line 14) and La Defense (15 minutes on RER L). I don't see direct trains from Saint-Lazare, you can search for them yourself for a specific date on the SNCF website.
Can you get to Gare Saint Lazare from Gare du Nord?
@Elena: Yes, you can go from anywhere, Saint Lazare station is in the city center.