If it's helpful,
Census Reporter developed a service to compute 2020 and 2010 population for neighborhoods and other local non-census geographies. All we need is a shapefile, or, preferably a pointer to a publicly accessible shapefile/geojson. If you provide us a link to a public map, we share the results publicly on
https://censusreporter.org/2020/ When we launched, it was self-service, but that was slightly bumpy, so it's by request now. No guarantees, but turnaround is generally within one business day, unless I'm on vacation :) The code is public on GitHub, but it basically works by assigning blocks to the user-provided geographies that contain each block's centroid/internal point. If the map aligns with a Census place, I also run a little audit process against the 2020 redistricting data population totals, and in the rare case that there's a serious mismatch, we include notes about it on the pages linked from above.
A very brief look didn't turn up a straightforward GIS file for LA "neighborhood councils," but if you have them, use the link on the above page to submit a request.