Most tulips sold are produced vegetatively and not by seed, so there is the ever-present possibility of inadvertent viral propagation along with the propagation of the tulips, just as there is for lilies. Also as in lilies, there are viruses that are debilitating or fatal for tulips and ones that can be tolerated. Some are transmittable across the genera, some are not.
I wish I knew more about the frequency of viruses in tulips, but I know very little. Botanical tulips without a cultivar name attached are likely grown from seed, and therefore should be free of viruses, unless they contract the pathogen in the three years or so that it would take to grow to salable size. I have botanical tulips that seed around my lilies, and think nothing of it.
Assuming the frequency of viruses in tulips is similar to that of lilies (this is the unknown pivotal point), I see no practical difference between in viral introduction between adding tulips or adding more lilies. But yes, when one compares the possible ramifications of adding tulips, as opposed to an unrelated plant that cannot carry transmittable viruses, then tulips would be a poor choice.
