Transportation from Gare de Lyon to Orly Airport?

Taxi should be 35 EUR fixed price, at least that is what it is from Orly to Gare de Lyon. Most other public transit involves several changes, ex: RER A to RER B at Les Halles to Anthony, then the Orlyval train, or 3 buses, etc.

Assuming you don't have huge amounts of luggage, the easiest route by public transport is to walk across the river to Gare d'Austerlitz, then take RER Line C to Pont de Rungis station (NOT the previous one Orly Ville) and a non-stop shuttle bus to the airport. Fare is euros 6.15

The absolute cheapest way, although very slow, is to take the Metro to Villejuif-Louis Aragon, one of the southern extremes of Line 7, and then get tram T7 to the airport. Cost is two normal Paris transport tickets, one for each leg.

I'm thinking it might be 3 t+ tickets, since Orly is in Zone 4, but it still is not very practical route. Either walking over the bridge to Austerlitz, then up the stairs to the No 5 Metro, then a change to the No 7 at Place d'Italie to get to Villejuif Aragon. Or take the No 1 or No 14 Metro to Chatelet, navigate the underground maze to the No 7 platform.
Take a taxi.

I'm thinking it might be 3 t+ tickets, since Orly is in Zone 4,

Zones have nothing to do with a t+ ticket used on the métro or on the tramway. Métro 7 (including any métro connections to line 7), connecting to Tramway 7 for ORY requires only 2 tickets t+.

I take RER B and the OrlyVal. If you buy a combined ticket it's about 12 euros. I've heard some bought just the RER B to Antony then had to purchase a fairly expensive ticket for the Val. I believe I've taken it from Gare du Nord, and either Chatelet or St. Micheal. I'm not sure which stop is most convenient to Gare de Lyon? You get off the train at Antony and follow signs to the OrlyVal. It's faster than getting to CDG but I think 30 minutes is a little optimistic.

But you still have to get to Les Halles on the RER A, take the elevator or escalator to the mezzanine, then walk to the elevator or escalator down to the RER B platform to go toward Antony. 12 EUR pp is 24 EUR. Take a taxi for 35 EUR and make your life easy.

Any way you go via mass transit, specifically, the RER, will call for at least 10 minutes of walking. If you have light or no luggage, maybe go for it but I am team taxi all the way. Unless your French is good, I suggest that you give the driver a piece of paper with your destination and 35€ written on it upon greeting him or her. I have been reading more stories lately than I used to about taxis ripping off customers. This way the driver knows you know the fixed fare.
By the way, by mass transit, it should take about 50 minutes assuming no stoppages and by taxi, assuming no traffic (a pretty big assumption in Paris on a weekday), about 25 minutes.