When Billie Lurk turns against Daud, if she were to kill Daud would that mean all of his assassins would lose there powers since they only have them because he shares them?
Although it is never explicitly mentioned there are several opportunities here. It could be the powers Daud's assassins have gained from him and through his training have become learned and do not depend on him being alive, this may at least be true for some of the basic abilities like Blink if not more advanced powers.
The other possibility is that Billie is able to gain power from another source, either from Delilah who has a link to the outsider, or from the Outsider himself. Given his perchance for drama, the outsider would be most entertained if Daud were to fall to the hands of one of his closest allies and may reveal himself to Billie to offer her the same powers he did to Daud allowing the assassins to keep there powers under a new master.
If the outsider chooses not to reveal himself it almost certain the Billie Lurk would seek him out given her fascination especially if it now fell to her to lead and empower the other assassins.
This is all hypothetical by it is mostly inline with what we do know from the lore.