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If not they may not have been wired in, if so the relay for them is probably shot.
You didn't post a year model, After market? stock? remote starter.
The relay, if used for used/needed for your model would be in under the dash with the remote starter itself (after market). If "stock" you'd probably need to reference the wiring diagram for it.
I'm assuming you didn't wire this remote starter yourself...? I'd try to find the wiring diagram for the remote starter kit that you used. When I installed mine there was 1 wire that I had to run up behind the headlight switch to activate the lights when I started it remotely. Check for a wire that got tapped up there and more sure the connection didn't somehow get broken. If still intact, as Dan said, you might have a bad relay. Some units have internal relays (like mine) so if thats the case with yours you might be kind of hosed. Which make and model is the your remote starter?
If its a "Bulldog" remote starter their web site has great wiring diagrams for each make/model. You will need the model of your starter to but can probably figure it out even if your not sure what one it is.
Some starters come with a rack with 3-4 relays on it to be used for lighting and door locks, power windows and such. Some do not come with any and must be bought separately when needed to make extra stuff function.
The starter turns on the lights with one of the relays until the key is turned on, then the lights are no longer under control of the remote starter. I would check the wire connecting it to the lights as Chris pointed out and while your under there just replace the relay/s, its just a standard relay, nothing special about it and is readily available at any parts store.
It may also be that the control box itself is failing to turn on the lights, you could test that lead for output once you know what wire it is from the wiring diagram. If that the problem you'd need to replace the starter or just use it as is.
If it was installed with a "T-harness" it will make any work you need to do much easier.