Controlling weeds in a ground cover can be tricky. There are herbicides that can safely be used in liriope and in your case you say that the species is spicata which is good to know because some herbicides are meant for the species muscari and not for spicata. For your bed, Acclaim, Fusilade and Ornamec are safe to use "over the top" in controlling existing grassy weeds. Basagran is also safe to use and it is used to control exisitng grasses and some broadleaf weeds. In any case you need to read the label regarding application methods,timing and mixing for best and safe use of the product.