Anti-aliasing is a technique used to make shapes and lines appear less jagged in pixel based graphics. Anti-aliasing is only a part of some of the algorithms that Lightroom and other professional applications deploy when upscaling images. Considering the fact that you are really trying to generate (passable) information that wasn't there in the first place, there are limitations to upscaling images.

Lightroom doesn't have the same advanced algorithms that other applications dedicated solely to upscaling images have, so you will get better results if you upscale to a multiple of the original width and height; 200%, 400% etc. Photoshop will allow you to pick between a handful of different resampling algorithms, but Lightroom will intelligently pick behind the scenes.

If you are looking for a better implementation of upscaling, that is a question that has been asked before:

* http://photo.stackexchange.com/questions/76054/best-software-for-upsampling-to-about-2x
* http://photo.stackexchange.com/questions/18468/how-can-i-upscale-a-low-res-image-to-make-it-appear-higher-res
* http://photo.stackexchange.com/questions/29854/how-to-scale-up-a-photo