I have had a Leupold 4x scope one my Winchester mod 70 featherweight 30-06 , in a Weaver pivot mount, since 1963 when my dad got it for me. It has always held zero with no problems. I honestly do not see the need for such a high powered variable on a lever action, and would recommend a much lower power scope such as Old70 and ruraldoc mentioned.
I would think a larger scope like most 4x12 models would add too much weight and upset the balance making the rifle rather unwieldy.