By the very nature of the Church as the Body of Christ ensouled by the Holy Spirit and guided infallibly by the teaching authority of the Pope and the universal Magesterium, the text of Lumen Gentium MUST be a coherent extension and illumination of Tradition. To reject that is to reject the very Tradition of the Church that one seeks to uphold by rejecting the validity of Lumen Gentium. It's a little ironic, but such is schism and heresy.
"the text of Lumen Gentium MUST be a coherent extension and illumination of Tradition."
Why? Have you read it?
While there are many excellent passages in it, these are often hedged about by ambiguities, circiterisms and novel propositions which have no basis in either Scripture or Tradition. You don't have to read further than chapter 1, para 1 to find them.