Rue cler area to get to Paris gare lyon

You can check for this kind of thing at www.ratp.fr/en. You would have to take two metro lines. Line 8 to Madeleine and then change there for Line 14. If you are willing to take the bus, then Bus 63 is an option. You would catch the eastbound bus on Quai d'Orsay near Rue Nicot and take it to the end of the line.

Mauve Line 8 (Direction: Creteil) from Ecole Militaire / La Tour Mauberg to Concorde, then
Gold Line 1 (Direction: Chateau de Vincennes) from Concorde to Gare de Lyon

OR

Mauve Line 8 (Direction: Creteil) from Ecole Militaire / La Tour Mauberg to Madeleine, then
Purple Line 14 (Direction: Olympiades) from Madeleine to Gare de Lyon

What time of day/week do you need to make this journey?
The bus is significantly less hassle (no stairs to negotiate, and especially not TWO sets of stairs with having to transfer from one line to another). And anyway more fun usually as you can watch Paris go by as you travel mostly down the boulevard St Germain. But it takes a little bit longer and depending on the time of day you're going, may be less frequent.

Or you could just pull out your cell phone, click on your Uber app and leave the navigation to somebody else.

If you have a data connection while you're in Paris, yes!

Our train leaves at 9:37am. So. Want to e there at least 30min before on Wednesday the 6th

According to the RATP trip planner, for an arrival at Gare de Lyon at 9:00 am on Wednesday Sept 6, going via the 63 bus would take 38 minutes.