Doesn't PS5 already have a lower priced sku of it's own? Rather ironic you're speculating about things based on rumours of prices and an unannounced system, yet conveniently overlook something that's already confirmed.
Lockhart, whatever it is will still share the same architecture as the Series X, and still be considered a next-gen system. No different to Xbox One X or PS4 Pro from this gen in that respect.
Revenue made on console sale prices matters very little (see: Nintendo profit margins). What matters most is getting your system in people's homes. So yes, Xbox gaining more market share would be worse for Sony and good for Microsoft.