I've had a hoarse voice for over 3 weeks and there is a small lump on m y thyroid. Could this be related?

See ENT. Hoarseness may be due to either functional or organic causes. Absence of cold, hoarseness persisting for more than two weeks .This is especially important in risk factors for head and neck cancer (primarily tobacco and alcohol use), or worrisome coexistent symptomatology such as severe cough, hemoptysis, unilateral ear or throat pain, odynophagia, dysphagia, or weight loss .
Possibly but unlikel. Nodules of the thyroid can cause hoarseness by affecting the recurrent laryngeal nerve that is near the thyroid. An ENT would be able to see that one vocal cord is not working well. However, this is a rare problem related to thyroid and usually requires a large nodule, that is typically malignant. Your should see an ENT for further evaluation.
YES. Something is going on this area. Can be from your throat or "voice" cords or from your thyroid. Most of the times a biopsy of the lump will rule out undesirable findings.