Although it’s rare, if you are taking higher-than-usual doses of thyroid hormone replacement medication, and it’s not reducing your thyroid levels accordingly, you should be evaluated not only for gastrointestinal issues like malabsorption, but lactose intolerance as well.
Also, keep in mind that most of the levothyroxine drugs do contain lactose, and some people who are lactose intolerance can react to the medications. Synthroid brand levothyroxine, for example, contains lactose, but competitor Levoxyl does not.
Source: Muñoz-Torres, Manuel, “Thyroid Lactose Intolerance Revealed by Severe Resistance to Treatment with Levothyroxine," Thyroid, Nov 2006, Vol. 16, No. 11 : 1171 -1173