Firstly, we analyze how the lace feels. This isn't necessarily possible over the internet, but when you're shopping at your local crafts store, it's a must. You or someone you know will be wearing this, it needs to feel soft, or at least wearable. The number one problem with bad quality lace is that it is itchy, scratchy, and just overrall unpleasant to wear. The softest lace is cotton lace, which is only slightly more expensive than the other types of lace. There are some synthetic laces out there that are mostly soft, and they are usually more or less acceptable. Some pickier customers won't accept anything but nice lace, though. Most eyelet lace is cotton lace.
Thirdly, and sometimes the easiest, is to read the materials list. On most websites, they list the materials used, and occasionally even list the type of lace they use. Raschel lace is typically a no-no, cotton lace is good. For sites that only list a general list of materials, usually when they just say cotton, that includes the lace, too.
Fourth, and this is probably the best way to learn, is to contact other lolitas and ask them. They can show you many examples of good lace and bad lace, the likes of which would absolutely choke this article. Ask lolitas whose style you admire, who you see as being very experienced, and have been involved in the style for a while. Most of them are more than happy to prevent you from buying a disaster!
Lastly, if in doubt, check the pictures! If you still can't tell, then you might have to pass. If you don't mind having "bad" lace on your dress, then go ahead.