If you wish to keep the old ceiling then you will have to try to repair it with the expectation that it may not work and will need replacing.
I have repaired quite badly sagged lath and plaster ceiling in the past where because of National Trust requirements they had to remain.
There are 2 possible problems:
The broken or detached laths where the plaster is still attached,
The laths or the plaster (mud) has detached from the laths,
This fix is not guaranteed to work but may give you the best chance.
Both problems require the ceiling to be propped from underneath to get the ceiling back to its original position with the least amount of further detachment as possible. Not so bad as long as it stays together and does not fall in a heap on the floor (quite a possibility).
Once the ceiling is propped you need to support it in position from above.
First I would clean off all the excess mud that has oozed between the laths and rake out the mud between the laths over the effected area, clear away as much dust as possible. Dampen down the entire area with a wet brush get right in between the laths. Then pour a very sloppy mix of cornice adhesive over the area with a brush work it down between the laths. Then lay off cuts of plasterboard over the area wiggle it around to get a good key to the cornice adhesive. Then using either fiberglass tape or sisal dipped in the cornice adhesive and lay it over the joist and spread about 200mm either side of the joist.
If you use fiberglass tape use a quadruple layer. Pour the rest of the mix along the junction of the ceiling and the joist.
Remove the props the next day and it should all remain in place. Now you can rake out the cracks and repair them like normal.
Bit of work involved but if it works you keep your old ceiling. Mind you I would consider replacing the ceiling if it does not mean a big deal to keep the old one.
Cheers Rod
__________________ Do not use fibreglass mesh tape on butt joins, ceiling joins or fibre cement sheet products EVER GREAT PLASTERING TIPS AT | 
