It's true that some vintage glass cups or mugs may contain trace amounts of lead on the outer surface or rim. This is especially the case with leaded crystal vessels, which were commonly used for more formal occasions in the past. For this reason, it's best to use those for decorative purposes and avoid drinking out of them on a regular basis. You can store craft supplies in them, use them as a vase, or fill them with toiletries in your bathroom, instead!
Today, most manufacturers stick to a strict lead-free policy when creating their glass coffee mugs. This information should be readily available in the product description. If it isn't, then you can reach out to a representative for clarification.