Hi Sally,
Yes you can reprogram the remote. Since all of the remotes have to be present during programming the one that you lost will cease to work anymore. Here is the program procedure for an 06 Corolla >>
1. Make sure the key is out of the ignition, drivers door is open and unlocked.
2. Insert the key all the way into the ignition, pull the key out. Repeat. (2x)
3. Close the drivers door, open it. Repeat (2x)
4. Insert the key all the way into the ignition, pull the key out.
5. Close the drivers door, open it. Repeat (2x)
6. Close the drivers door.
7. Insert the key into the ignition, turn to on (do not start the engine), turn to off, remove key.
8. The door locks should cycle to indicate program mode.
9. Press and hold the LOCK button on the key fob, press and hold the UNLOCK button, release both buttons, press LOCK again.
The door locks should cycle one time if the programming was successful, if they cycle twice you'll have to repeat the previous step as the programming didn't take.
As for the locks, that is really up to you. They do not actually have to be replaced, a Locksmith could rekey them for you but then you would have to use a seperate key for your doors. You could go all out and have the igniton rekeyed as well but then you're looking at new (chip) keys and that's even more $$$.
I think you'll be just fine having the key and remote reprogrammed, yeah the thief who stole your keys could possibly still open the doors to your car but it's impossible for the ignition to start. If it really bothers you though, do check with a Locksmith. You can have those locks rekeyed for much less than $700.
Hope that helps!
Mike