The smaller Lockhart doesn't necessarily need to be less powerful. If you look at the size of the series x and consider how large a UHD Blu-ray drive is then remove that drive you would end up with a console about the size of Lockhart.
If it uses the same split motherboard design and it likely does then everything should fit just fine in this smaller variant.
I mean...if they were going for a less powerful version they could make it basically the same specs as the ps5. Now imagine that selling for $199-$250. Microsoft would end up crushing Sony in the long term. I think no matter what Microsoft does, chances are Sony will be ahead for at least the first year but in its 2nd Holiday assuming Microsoft makes good use of its studios and delivers on the exclusive front then it's 2nd holiday season which would be 1 year after launch we will see a switch to the Xbox becoming a serious threat to Sony and begin catching up and then surpassing it by its 3rd holiday.
Of course if Microsoft drops some big bombs in July and comes out $100 cheaper (or potentially more than $100) then it's possible that they could come out of the gate even and then at the 1 year anniversary the Xbox would begin to surge ahead as they bundle games for the holidays as they always do and also sometimes do a temporary price cut with those bundles along with special edition consoles etc.