Running a fund and an AngelList syndicate at the same time presents a number of problems.
First, most LPAs prevent managers from working on multiple funds at the same time because managers have fiduciary duties to their limited partners, such as the duty of care to act prudently, prioritizing beneficiaries' interests.
Second, there are conflicts of interest around investment decisions that arise from having two funds in one focus area, since a manager may choose to cherry pick deals or feel pressure to invest in deals with companies that are failing to save the company.
Third, there are issues around the time and attention that a manager must place on the respective funds that detract from time and attention required for the the other fund, such as when diligencing deals, working on reports, or managing operations.
These various problems can be overcome by disclosing everything to limited partners up front, having a limited partner advisory committee to clear conflicts, and providing full transparency during operations, but this can be time consuming and difficult for a manager to do, and may also make limited partners skeptical.