Hi, and welcome to the awesome world of blue-tongue skinks. At least I hope you decide to get one as they are simply the best pet lizards available.
As to the lid, a 125 gallon tank is in all likelihood high enough that the skink will not be able to climb out. They are not jumpers at all, so as long as the sides are higher than the skink is long, it'll be escape-proof. You may still want a lid for heating purposes and, of course, to keep other pets (cats) out.>>Hello! I have been researching blue tongue skinks as I have been interested in getting a reptile soon.
For detailed, comprehensive information on BTS care, you may want to write me directly and I'll provide with lots of it, including excellent online sources.
Good luck.
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Edward
Carpe diem