Horn disturbs controller and lcd on common power source
Three main suspects:


Supply decoupling / filtering: use decoupling capacitor in all ICs power supply lines. Follow the datasheet guidelines for each device.
Grounding: your schematic shows somewhat careless grounding. Use a ground plane and/or single point ground.
Piezoelectric effect in ceramics capacitors: If the PCBs are close to the horn, the vibration induced by the 105 dB SPL levels can wreak havoc in ceramic capacitors. As this kind of capacitors are everywhere (coupling, decoupling, filtering, timing...), it's very likely this could be the main cause of the glitches you're observing.


How to mitigate the piezoelectric effect?


Acoustically/mechanically isolate/decouple the PCB from the horn. Don't attach the PCB to a stiff surface that can couple to it the vibrations caused by the horn. Also, use acoustic foam around PCB to reduce SPL levels, put it inside a box, etc.
Replace ceramics with equivalent electrolytic and film capacitor when possible and convenient.