Export problem with light ray effect

Did you want assistance with the image quality or the file size?

And you're saving an Animated GIF, correct?

An effect like CC Light Rays will look best with a higher color depth.  When you export as a GIF, you're reducing the color depth that you're working at in AE (probably 8 bits per channel, but AE support 16 bpc and 32 bpc) to 8 bits total or less (a GIF can be saved with as few colors as 2 and as many as 256).

Unfortunately, AME doesn't give us a lot of options that should be available when saving a GIF file as it's heavily slanted toward video file formats.

If anything, I'd recommend that you render your lighthouse animation at Best Settings / Lossless and then import the resulting file into Photoshop (keep the duration under 500 frames total as that's the maximum number for frames that PS supports in an Animated GIF).  Then choose File > Export > Save for Web (Legacy).  In the Photoshop Save for Web dialog box, you'll have complete control over all GIF options, allowing you to find the right balance of reducing the image size and the color depth to achieve the desired file size.