LM Studio explains how downloaded models can run without the internet. You need a connection to download the application and models, but the conversation itself can then happen on your computer.
First, choose a local model and check that it starts. Then disconnect from the network for a while and ask for help with a simple, non-sensitive text. If the model still responds, you get a concrete sense of where the work is happening.
For a writing session on a train or in a cabin, this option can be valuable. You will not automatically get fresh web answers, of course, but you can keep discussing wording and ideas. That can be enough when your goal is to move forward with something of your own.