I am booking a 1w ticket and need to get to Lyon to meet some friends. Unfortunately, BA only flies from Gatwick to Lyon. So I have the following options:

1) Transfer from LHR to Gatwick and then fly directly to Lyon.
2) Fly from LHR to Paris and take a train Lyon.
3) Fly from LHR to Geneva and take a train to Lyon.

Does anyone have any suggestions? I am looking for the quickest way possible. I am flying into LHR first thing in the morning from Bangkok and would like to get to Lyon by midday if possible.

Thank you in advance for any suggestions you have.