I may not know all the details about this lockout but this is what makes sense to me.
Allow each team to have a range in majority profit splits. Perhaps make the BRI range 47% to 57%. This should allow smaller market owners to offer lower majority profit split with players and allow them to produce more profit in order to grow their organization. It will also allow larger markets to continue as they wish, if they wish to continue offering players higher percentage.
When you first start your career you usually do not get an extremely high paying job, unless you are an all star. A smaller market owner with majority ownership may have the capital to invest in all-star player with the new BRI in his organizations favor.
A 50/50 split is ideal if you are a conference wining team or perhaps 43 owners / 57 players split because they are producing results and increasing profits with their performance.
Also perhaps owners and players can come to some sort of agreement in profit splits based on the sales of each basketball related products. For example memorabilia can be higher split for owners since it's something that can sell all season long, and ticket sales can have a higher split for players since the fans are coming to see their team.
These are just some unorganized thoughts on the current situation, perhaps someone can take find this useful, or perhaps for the next lock out.