Thank you very much :)
The reason I’m asking about Cyanogen versions is that 10.2 is based on Android 4.3. Between Android 4.2 and 4.3 a lot changed regarding the Bluetooth stack. If you have CG earlier than 10.2, updating might make the software problems go away.
Can you give model numbers and Android versions for the LG phones? Again if they can be updated to 4.3 I expect the issues will disappear.