It depends how well MS market this with devs and gamers. If Lockheart is made so that all it does is play games exactly the same as series X but just at 1080p instead of 4K then obviously its not going to hold back any development. It would be a shame if it did, but I think MS will have worked hard in this regard.
If MS market this well to consumers they could have the gen in the bag, no matter what Sony do. If both PS5 and Series X launch at $499 then PS5 will for sure sell the most out of those, but MS will have more sales and more production when including a, say, $299 or $349 Lockheart. We already know Sony plan to sell 2m less than PS4 in the first two quarters, I expect they're going to concede an early lead and perhaps a fairly big one if they don't reconsider, regardless of how well Lockheart is received. This is just from the fact that all production will be sold through especially for a cheap new gen console and MS has the means to produce way more with two different models. Then when Xbox is ahead and has the market share lead, plus way more exclusives than this gen since they bought all the new studios, they have the driving seat and probably won't look back.
On the other hand, if MS get the marketing wrong and/ or Lockheart does handicap xbox's next gen games then Sony could easily romp to victory again. If PS5 is cheaper than XSX then Sony have some power, but if they're the same price I think MS are fully in the driving seat and its their gen to win or lose. Launching two models at the start of a gen is either brilliant or a really bad idea, I don't see it falling anywhere in between.
From a gamer's perspective I really hope MS gets this right, Lockheart seems like the perfect second console to pick up to play xbox exclusive games like Forza, especially if it is more than $200 cheaper.