It's a wonder what one can do within 6 hours in Paris. About three time so far I've done that with arriving at
11.30 am and departure at 6.20 pm.
If you're goal is to go up Tour Eiffel go there first and have a look at the lines, if you see that they are not too long then head up, if the waiting time is too much go to Tour Montparnasse and go up there. Note that they have airport style security, so you need to store your baggage somewhere at the station before you even plan to go visit the city.
From Tour Monparnasse you can walk through Jardin Luxembourg, Notre Dame and along the River Seine back to Gare de Lyon.
From Tour Eiffel it's also a nice walk along the River Seine, or even an idea to head to Arc de Triomphe then along the Champs Elysees to Concorde and then through the Tuileries Garden to the Louvre, City Hall and finally Notre Dame.
For lunch maybe buy a big sandwich to go at the Station because close to Tour Eiffel there is not much to eat (beside the expensive choices inside the Tower itself)