The "radiation" that results in long term damage to film isn't the sort that lead-lined bags protect against.

It is cosmic rays that cause the damage, and unless you have your own, very deep salt mine, there really aren't any steps you can take to protect film from them.

40 year old Tri-X will probably have lost some speed, and have a fair bit of base fog. It is worth experimenting with, but the effects of age are unpredictable.