Yes, I've wondered what was going on here. But now I've given it some thought, here's my take on it:

Lucy is the receptionist. That doesn't mean she necessarily needs to handle emergency calls. Where I live (in the UK) police stations have their own non-emergency numbers and would have a reception desk.

So, someone might call the Twin Peaks Sheriff's Department non-emergency number and speak to Lucy. This could still be serious police business, like if somebody had some information about an ongoing case or wanted to speak to a police officer but it's not an emergency.

This makes perfect sense because they don't want the emergency line to get clogged up with calls that are not emergencies. In the UK, we even have a standard number for non-emergencies: 101, whereas 999 is for emergencies.

It only looks strange to us on Twin Peaks because we never saw the back office in seasons 1 and 2. Perhaps they got the extra staff after things started going crazy after evil Cooper escaped from the Black Lodge.

But in 21st century policing, having an emergency desk and a non-emergency desk is nothing unusual. In fact, I'd say it's essential.

Essentially the same in U.S.

Yes. The back room is what is referred to as "dispatch," and maybe another line for somewhat different operations. Contrary to popular opinion, advancing technology doesn't always reduce the number of necessary jobs. Since more things can be done, more people are needed to perform the operations. I suspect the Twin Peaks sheriff department broadened  its capabilities during the last 26 years, and hires a few more people than we saw in the 90s. But it still needs its friendlier and more 'front-end" type of employee, Lucy, who greets and transfers.