Could an eating disorder cause low t3 (liothyronine) thyroid on blood tests? how?

Non- thyroidal : Yes, this sounds like what was called"euthyroid sick syndrome. The thyroid labs look confusing, low or normal TSH and low T4 & t3 (liothyronine). Associated with starvation( eating dis)., serious medical illness, icu, etc. There are complicated explanations involving the body's attempt to re-regulate metabolism while conserving energy in a crisis. It will normalize as feeding/consistent nutrition returns.

Yes: Malnutrition, as can occur with an eating disorder, can cause a disturbance in the way the body assembles important chemicals like thyroid hormone. Eating disorders can be deadly, with up to a 25% mortality rate in untreated cases.