Yeah, a Team lead largely is more responsible for technical decisions, not so much managing the team. But, as Mister points out, each time you go for a new TN, your job description must be listed accurately, regardless of the internal title.
if your functions have not chnge in the meantime, just the proportion, then there is no need to get a new TN just for that.
But be aware, if you were promoted to a supervisory position, you may no longer be eligible for TN.