Weird, the NIC site of Liechtenstein says it's not registered
Trying to check if I could make it resulted in "this domain is invalid" though. Apparently, it is too short. (Lo.de works for some reason though...)
Lovelo.li is available, still.
Other 4 non . urls also weren't permitted, so it's not something lo.li specific.
Liechtenstein seems to require at least 3 letters for the url to be valid.
You could either try to convince the Liechtensteiner domain authority to revise that and allow 2 letter .li's, then snatch the domain, or use a prefix and end with lo.li