Cell phone bluetooth range
There are fundamentally two ways to increase the range of a wireless link:


increase transmit power
improve receiver sensitivity


With a bidirectional protocol such as you have described, then a problem with either the transmitter or receiver would cause the link to fail.

To diagnose a range problem on a link it is common to run some type of bluetooth packet sniffer / protocol analyser on both sides of the link, e.g. wireshark on a PC or android bluetooth snooper. By matching up the logs from both sides it should be possible to see which device is attempting to transmit but not being successfully heard at the other end. The goal is to determine whether it is your transmit power or receive sensitivity which is letting you down.

side note.. An LNA is usually considered a receive device. The amplifier on the transmit side is usually a PA.

and yes, it is possible to get a couple of dBs improvement by matching the antenna, but that depends on how bad the antenna match is to start with.