I drove past LAFD Station #1 today, and noticed that the US Flag was NOT at half staff. Since a Lee County firefighter died, does the LAFD not recognized it by lowering the flag or was this just an oversite on the FD?

According to federal law, only the President of the United States, a state's Governor, and the Mayor of the District of Columbia can order the US flag lowered to half-staff.

If everyone were to half-staff the US flag at will, the symbolic value of that honor would be lost. Another option is to display black crepe near the entrance to a building, perhaps with a photograph of the former mayor, firefighter, police officer, etc.

That very well could be.

Station 1's flags were at half staff yesterday. I know this because I put them there when I went on duty.