Generally what's happening is that when a phone can't detect a cellular signal, it boosts both the incoming antenna signal and the outgoing signal to their maximum power levels in order to try and detect a cell tower or connect with one. So yeah, the fact that it can't find a cell tower means it's going to be trying its hardest and using up your battery rapidly.
Modern smartphones usually have a way to switch cellular data on and off, and as it turns out, there's a similar feature on your phone. It's called Standalone Mode and disables calls, Bluetooth and web access (cellular data). Here's how to turn on Standalone Mode on your phone, according to the [link|https://theinformr.com/downloads/phones/manuals/lg-vx-8500-manual.pdf|Chocolate by LG User Guide|new_window=true].
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Unfortunately they've tied Bluetooth into that control, so if you're using Bluetooth headphones you'll have to switch to wired headphones, but that should take care of your power drain issues.