Technically speaking, probably not. The Lions organization (or someone) presumably owns the copyright in the logo, and the Lions or the NFL also presumably have trademark rights in the logo as well. The licensing of NFL logos for shirts and other gear is big business, and the rights holders would say you must pay for permission.
That said, and speaking more generally now, if someone uses an NFL logo on a single article of clothing for his/her own personal use only, I suspect it might be considered fair use under copyright law and mere ornamental use under trademark law (meaning okay to do). Both arguments are subject to good counter-arguments, however, and the NFL/Lions would undoubtedly disagree if pressed to respond in court.
All in all, I think the real world legal risks of using a logo on one shirt for purely personal use are small. It may well be infringement, but the likelihood of the NFL or team being aggressive enough to enforce IP rights against a single fan in such a situation seems very remote.
The information provided here is general in nature, is not legal advice, and does not create an attorney-client relationship with Will Montague or Montague Law PLLC.
one personal use on a personal shirt not transported or sold in commerce does not generally involve commerce that can be regulated by the federal government under the commerce clause and thus does not invoke Federal trademark law. in most states it also does not invoke state trademark law. So, it's probably legal. Do a second one for anyone else and you have generally crossed the line, especially if there is any commercial purpose to that second shirt.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
I would just add three comments to what my colleagues have posted.
1. If your source for the logo is an authorized iron-on decal or patch or fabric, and you put the logo on a shirt for your own personal use, you should be fine since you would be using an authorized product in a manner in which it is intended.
2. If, on the other hand, you copy the logo off the internet and try to have a t-shirt manufacturer make the shirt for you (with you supplying the artwork), you are going to have to represent that you owner or have permission to use the logo, which you do not. So, you need to think about that and pay close attention to any terms that you agree to when you submit the artwork. (Some manufacturers refuse to print any artwork that they know is protected by copyright and/or trademark law.)
3. From a practical standpoint, it you simply prepare and wear the shirt and don't post (or allow others to post) pictures of you in the shirt on fan pages, etc., the chances are pretty slim that you would come to the attention of the owners and/or authorized licensees of the relevant rights. But, there are no guarantees.
Any answer or other information posted above is general in nature and is not intended, nor should it be construed, as legal advice. This posting does not create an attorney-client relationship between you and the posting attorney, and you are urged to engage a qualified attorney who is licensed to practice in the relevant jurisdiction.