The easiest way is to go to a visa agent. Yes it will cost you but everything will be done. No worries. It is true you can do it yourself for a lot cheaper but you probably end up fustrated. From the second year do it yourself very easy then
The first priority is filing a police report for lost documents. The next important is your passport as you will not be able to get a new bank book(passport) without passport. I renewed my Belgium passport a few years ago and when they issued a new passport they gave me a letter stating the reason for the new passport which immigration required. With the new passport and letter everything was in order with immigration for them to stamp the new passport.
As per previous comment it really sounds like you are confused about expiry date and 90 day report. You can only do a 90 day report when you have a valid visa or visa extension. In your case this expires Mar 15.
Normally all that is required is you valid drivers license from your country. You will have to provide a medical certificate, certificate of residency (which you get from immigration). You will have to watch a video and do a reaction test . Pay the fee and you will have a Thai licence. If you want to have a car and motorcycle license these are considered as two separate licenses. Plan accordingly.
My embassy issued a letter stating why they issued a new passport which immigration required. Also you will need to update your new passport with your bank.