Taking levothyroxine without a thyroid problem would be highly inadvisable. In a person with a normal thyroid, it could produce an artificial hyperthyroidism, and may produce a dangerous cardiac arrythmmia.
Levothyroxine is prescribed for individuals with documented thryoid conditions. I am not sure why you would take medication for a problem that does not exist. However, some medications originally developed for one ailment have been found useful for other conditions. Hormone levels that are not balanced may be treated with levothyroxine; but that should not be the first choice.
Taking levothyroxine without a thyroid problem should only be done under the advice of a physician. Typically levothyroxine is used to treat hypothyroidism (or under active thyroid) caused by diseases such as Hashimoto's disease. A blood test is typically given to test your TSH level and determine the correct dosage.
You shouldn't take levothyroxine unless you are HYPOthyroidic. You essentially would be making yourself HYPERthyroidic and could suffer from headaches, heart palpitations, nervousness, insomnia, and edema.