Despite looking grass-like, Liriope is not actually a grass, which is why grass-specific herbicides won't work well (if at all). Instead, if you need to use herbicide, a systemic (root-killing) treatment would be required, and those chemicals are non-selective, meaning they will damage any plant they come into contact with. Therefore, if the Liriope is intermingled with any other desirable plants, this would be challenging to use without causing damage to them as well, and physical removal (continued digging-up) instead would be the only practical alternative.

The only other option if you wish to avoid herbicide and the rigor of digging would be to smother the patch. Here too, the practicality of this depends on whether or not desirable plantings are intermingled with the Liriope. If they are, this method won't be feasible and you'll again be left with digging them up until they cease returning. Eventually, removing as much Liriope foliage as you can will starve-out the root remnants and the plants will stop regrowing. The creeping form of Liriope is pretty tough, though, so any treatment - digging or herbicide - may take awhile with repeated efforts to be able to finally eradicate it.

Miri