Can the negative be boost with LM2577? I found this positive boost scheme, what should I change for the negative?
The LM2577 is not designed for negative output applications, and is not readily adapted for such use. A different topology (arrangement of switch, diode, inductor, etc.) is generally required for this task, which is not supported by this device due to its intended use with positive-output applications.
@frekkia
Here is an example of LM2576-12 from TI about negative boost configuration for your reference.
Also there is a design tips from TI about Designing a negative boost converter from
a standard positive buck converter.