That's really odd. I'd expect for it to lag when previewing, but not when it's rendered. If you've brought in the audio file as an MP3, that could be the cause. Make sure you're using a WAV or AIFF file.
Yup, no mp3's in AE. Mp3's are easy t convert to wav or aiff, and their file sizes are teeny-tiny compared to video. Just don't use them. If you don't convert them an you have problems, you only have yourself to blame. You've been warned.
But now onto the REAL problem here. Read this.
And take it to heart.
Yes, as Dave mentioned too, avoid using MP3's.
However, I don't know that your real problem is your output file being too big. I viewed it via your Facebook link and it still stuttered, but that file would have been compressed for web playback.
So I believe your problem lies elsewhere - maybe due to using an MP3.
Did you ever get this issue fixed? Let us know if you still need advice.