Some lilies are very tolerant of viruses. Most breeders select for that quality as one of their intended aims. Thus varying degrees of virus susceptibility/tolerance among lilies are inevitable. Merely because you have had a certain lily for years unscathed has little bearing on whether the lily is immune to everything.
I'm sure you've noticed how some lilies are more vigorous, or disease prone, or more insect prone than others? That is how some get "sick" while others don't. It's in their genetics. It is analogous to some human races being more susceptible to diabetes - it's in their genetics. When someone in you family gets sick, does everyone always get sick too, and at the same time and severity? Gosh, that would be a scary world.
Keeping your tiger lilies in a bed far away is good, but nothing is absolute. An aphid caring a virus can be blown around in a storm, for instance, coming from a mile away and land on your lily. Likewise you, a dog, whatever can become an unwilling carrier of virus or virus carrying insects from one flower bed to another. Not a usual circumstance, but it can and does happen, and in myriads of ways.
Working at a retail garden center, I often talk about bugs on plants with customers. Often I get asked "but where did they come from?" It's such a silly question. Apparently a lot of people seem to think their yards have an bubble impervious to all things bad surrounding each of them. NOT!!
Rick