Where in Lyon will be staying? That would help narrow down recommendations.
As far as reservations go, if you don't speak French, the easiest thing would be to pick a restaurant that has a reservation tool on their website. lafourchette.com may also be useful for making reservations. I would not recommend using email as a means of making reservations because it's pretty common for restaurants to not monitor their email accounts religiously.
If you want to go to a restaurant that doesn't take online reservations, you may find it easier to stop by earlier in the day (or the day before) and work through the process in person -- you may find that easier than being understood over the phone when the other person is trying to understand your fractured French with the cacophony of a busy restaurant in the background.
It's pretty straightforward (you would be in bold, the restaurant in italics):
Bonjour monsieur (or madame). Je voudrais réserver une table (I would like to reserve a table).
Pause, and they'll ask either when or for how many.
Pour combien de personnes ? (For how many people?): Pour deux personnes (for two people)
Quand ? (When?): Pour le quinze juin (on the fifteenth of June)
A quelle heure ? (At what time?): A vingt heures. (At 8 PM.)
Votre nom ? (your last name?): XXXXX (If you have an unusual last name, it's sometimes better to pick a fake name that would be recognizable to a French person so you don't have to spell it, as letters are pronounced differently in French than in English. Consider "DuBois" [dew bwah] or "Bernard" [bear nahr])
You may hear the word complet (full) or indisponible (unavailable). Either way, say merci and move on.
If you're staying at a hotel, ask the desk agent or concierge to call and arrange for the reservation.
As far as how far ahead of time -- it depends on the restaurant. In a town the size of Lyon, you should have no problem making a reservation earlier in the day for the same evening, though you might need to try a few places if you focus on trendy or particularly busy restaurants.