My deepest apologies for the length of this post...
I'm sorry to have let this question sit for so long, but it's a pretty complex answer and I wanted to have some time to think about it. The short answer to your question is (you guessed it) it depends. On many different things.
Ownership in the dance world is a different situation than it is with art forms that have a universally recognized notation system (like music and theater), or where the work itself is a corporeal item separate from the artist/creator (like most visual art) Paintings and bought and sold all the time -- ownership confers rights of usage and attribution. I don't know where you are, geographically, but if you've ever been to the Frick Museum in New York City you've probably seen the Holbein portrait of Henry VIII. It's one of the most familiar images of the king around -- I've seen it in cheap history books, expensive journals and everywhere in between, and almost always it comes with its little caption ("courtesy of the Frick Museum" or something similar)
A play or a piece of music is usually copyrighted to the author or composer (or their estate), but those rights are often administered by a publisher. Dramatists Play Service is the home for Thomas Babe, J.M. Barrie, S.N. Behrman, Samuel Beckett, Lee Blessing, Eric Bogosian, Carol Burnett (yes, the comedian -- she co-wrote a play with her daughter), and a specific translation of Beaumarchais' The Marriage of Figaro. And that's just a few of the 'B's. Not all authors use a service, and some works are in the public domain (though certain translations might not be) But as US and international copyright law keeps extending the duration of the protection public domain is becoming much less common.
The control that the service administers can vary widely. In many cases it is simply a matter of royalty payments and credits -- you sign a contract that agrees to a specific fee and a specific kind of credit in programs/promotions. In exchange, often the service will supply the scripts (the official version of the text). Other artists have a more complicated set of requirements attached to the work -- they may govern the logistics of production (kind of theater, size of orchestra).
When we get to dance, we automatically step to the complicated side of the street. For most of its history, dance has been passed down person to person rather than through a text or other recording. Aside from the difficulties that makes in accuracy, it’s very hard to establish authorship/ownership. This is why we put so much emphasis on the antecedents.
I wrote about this a few years ago, in a review of Jardin Animee that was reconstructed from notation for the Pacific Northwest Ballet school. This posting is already pretty long, so I’ll just put a link to the review
hereif you want to take a look.
Because ownership is so tentative, many choreographers are very protective of what they can actually claim. Living choreographers often handle their contracts by themselves, have the right to refuse a work to someone for whatever reasons they choose, can require any one of a number of elements in a staging, and can make very specific limitations on how often (and where and for whom) a company can perform a work they have staged. Our local company is in the middle of a run of Jerome Robbins “Dances at a Gathering,” and many people have commented about Robbins’ protective nature. Peter Boal (the artistic director here) says that you “earn the right” to perform “Dances” by proving yourself in other Robbins works. Before his death, Robbins was the one who controlled this -- now it is done by his estate managers. Some choreographers willed their intellectual estate to a foundation which acts in their absence -- for others it’s usually a family member or close friend. Some works are very hard to acquire, others are relatively simple, some choreographers are very particular about who will stage the work and others are more flexible, but it’s almost always about a direct, personal contact.
Getting back to your original question (about Pharoah's Daughter) I don't know any particulars about this specific ballet or the Bolshoi's production, but yes, I imagine that the rights to the work remain with Lacotte unless he's signed them over to someone else. His agreement with the Bolshoi might include limitations/guarantees about which other companies might perform the work, how the work is maintained in the Bolshoi repertory, which dancers might be able to be cast in the work, etc. Since this is a fairly contemporary production, there may also be a stipulation about how many performance the company can do altogether -- just because a group buys a staging, or even commissions a new work. It's not necessarily the case that they get unlimited rights to all aspects of the ballet. (though I'm sure that they feel they should!)
Looking back over this it seems really long, and I'm not so sure I answered the question you've posed. If this makes no sense, don't hesitate to ask - I promise to be more succinct next time.