It look like that lake trout are susceptible, to a much lesser degree, to this disease according to the following articles.
Among species found in Utah, rainbow trout are the most susceptible, followed by kokanee salmon, golden, cutthroat, brook, brown trout and splake. Recent discoveries show whitefish may be infected as well. Lake trout may be infected under laboratory conditions and other game fish species such as bass, bluegill, perch or walleye do not get whirling disease UTAH
Conversely, Wagner et al. (2002) exposed lake trout to 1,000 tams per fish at 10 weeks of age and sampled at either 5 or 20 weeks. Interestingly, by PCR 100% of the 20 lake trout sampled were either positive or weakly positive at 5 weeks, as were 100% of brook trout. However, at 10 weeks by spore enumeration only 13.6% of 22 lake trout were positive, while 100% of the brook trout remained positive. Blacktail and whirling behavior were not observed for any of the lake trout, however, 9.5% did show cranial deformities. This correlates well with follow-up studies conducted at Leetown using labeled tams. Preliminary results suggest that the tams are able to attach and enter the epithelium of the lake trout but do not progress to infections of cartilage and development of mature myxospores. USGS