What people mean is that you should use strings okayed by the maker. Lever harp strings are not standardized at all, not like pedal harps. Some harps use pedal harp strings, some use much lighter stringing than that. It’s not so much a question of gut v. nylon as that you can damage a harp by putting, say, pedal harp strings on a harp not designed to cope with that much pull.
In your case I think you have a harp that uses pedal strings, right? A L&H, wasn’t it? No worries about damage in that case.