You can't. Minnie Vans no longer provide ground transportation from the airport: that service was discontinued with COVID and never re-introduced. Now, they only provide transportation around WDW property, and yes, you book a Minnie Van through the Lyft app.
https://disneyworld.disney.go.com/guest-services/minnie-van-service/ (*Caveat: Supposedly, club level guests were offered access to Minnie Van GT around the end of 2022/early 2023. I don't know if that's still happening, but if you're staying club level, it might be worth contacting Disney to ask about. At last reporting, it would cost a club level guest $200 for a one-way transfer ($400 roundtrip), and had to be arranged through Disney Signature Services no more than 60 days out.)
You can still request a regular rideshare (Uber or Lyft) from the airport. There's also Mears and Sunshine Flyer shuttles which provide services comparable to the former DME (sans luggage transfer), and if your budget is bigger, private transportation services.