Given that the screenshot appears to be taken in Alderney, I can't help but wonder if the lack of livery on the police car might indicate that they tried giving Alderney's police a separate livery at one point. Alderney is already indicated as being in a completely separate state from Liberty City, and SA already had separate police cars and livery for each city and the countryside. Maybe they tried it again for LC and Alderney and it didn't work? Just a guess.
EDIT: Even though these cars already resemble the LCPD/NYPD livery, there's still a resemblance between this and the squad car in that screenshot. This is the livery for the Hudson County Sheriff's Office cars in Hudson County, which is the specific part of Jersey that Alderney is based on.
The stripes on the almost-unmarked cruiser in that screenshot of IV almost look more spaced out between each other and closer to the window and bottom of the doors than the usual NYPD/LCPD markings, and more similar to the Hudson County Sheriff's. If I'm not just seeing things, then maybe at some point Rockstar was going to include a cruiser similar to this and then just gave up and used LCPD? Remember, too, Alderney police officers have different uniforms and hardly (if ever) refer to themselves as LCPD, with some even announcing themselves as "State Police." So the developers clearly went through the trouble of making the officers themselves different, but then they stopped at differentiating the cars?