Yes, a new Matrix movie would've happened eventually with or without Lana Wachowski
As jokingly teased in Matrix Resurrections, Warner Bros. wanted a new Matrix even if the original creators weren't involved

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The Matrix Resurrections Photo: Warner Bros.
There’s an odd meta moment early on in The Matrix Resurrections where Neo, stuck in a new version of The Matrix and believing that he is legendary video game designer Thomas Anderson (creator of a trilogy of video games called The Matrix), is summoned to the office of his business partner (Jonathan Groff’s Smith) and told that their studio’s parent company, Warner Bros., is going to make a new Matrix game. The implication is that it’s happening with or without him, a nod to the movie’s ongoing theme about binary choices that aren’t really choices at all.