Lilies produce a single growth shoot per season. Your damaged one will not do anything else this year but should return without issue next year.

As you have determined, lily shoots are pretty fragile things and easily damaged as they emerge. If you want to grow lilies with a rambunctious puppy/dog in the picture, you need to make sure they can't get access to the shoots in spring. Once the lily puts on some height, it is somewhat less vulnerable but not completely, so continue to protect somehow. Other plants surrounding it can do the trick or just a couple of stakes on either side of the emerging stems.

This is from the "been there, done that" school of gardening :-))

cheers... most of my lilies are protected, but some of the ones in large pots arent as i didnt think the little begger would climb and dig! plus they (got 3 small dogs) are usually supervised.