Lawrence is not easy to categorise politically. In his ideal political order,
...each man shall be spontaneously himself – each man himself, each woman herself, without any question of equality entering in at all; and that no man shall try to determine the being of any other man, or of any other woman.
That's partly in line with modernity (the emphasis on autonomy, on a self-determining individual) and partly not (the lack of interest in equality). Nor did he really follow through in an intellectually consistent way with autonomy - he recognised that there was a given nature that we either lived within or suffered the consequences of, and he thought too that we were dependent in significant ways on others (in marriage, in having a sense of a homeland etc.)
The upshot is that from a traditionalist point of view Lawrence is flawed but nonetheless still interesting - more so than most other modern authors (for me, his great appeal is that he writes as an embodied creature living within a created reality with spiritual meaning).
This is Lawrence, in Mr Noon, affirming a relatively traditional view of sex distinctions in which the aim is to uphold a sexual polarity between the masculine and feminine:
Ah the history of man and woman...the fatal bond that binds man to woman and woman to man, and makes each the limit of the other. Oh what a limitation is this woman to me! And oh what a limitation am I to her almighty womanliness.
And so it is, the two raging at one another. And sometimes one wins, and the other goes under. And then the battle is reversed. And sometimes the two fly asunder, and men are all soldiers and women all weavers. And sometimes all women become as men, as in England, so that the men need no longer be manly. And sometimes all men become as women, so the women need no longer be womanly. And sometimes - but oh so rarely - man remains man, and woman woman, and in their difference they meet and are very happy.
But man must remain man, and woman woman. There is something manly in the soul of a man which is beyond woman and in which she has no part. And there is something in woman, particularly in motherhood, in which man has no part, and can have no part. For a woman to trespass into man's extremity is poison, and for a man to trespass into woman's final remoteness is misery.
So there we are - the old, eternal game of man and woman: the time-balancing oscillation of eternity. In this we live and from this our lives are made. There is a duality in opposition, between man and woman. There is a dual life-polarity. And the one half can never usurp the other half - the one pole can never replace the other. It is the basis of the life-mystery.
Note that Lawrence felt that in his own time women had become mannish - not a surprising result given that by 1920 there had been 60 years or so of first wave feminism in England. It's to Lawrence's credit as well that he recognised that it is a struggle - a cultural achievement - to keep the polarity of men and women balanced, i.e. that it was not something that you could passively assume would always be there.
Lawrence went on to urge men to uphold their masculine side of the polarity - even if they came under pressure to give way:
For a woman doesn't want a man she can conquer: no, though she fight like hell for conquest...Ultimately, a woman wants a man who, by entering into complete relationship with her, will keep her in her own polarity and equipoise, true to herself. The man wants the same of a woman. It is the eternal oscillating balance of the universe.
Lawrence did not get everything right. His criticisms of conventional sexual morality seem misguided now, given what has happened following the sexual revolution. It's not that Lawrence wanted people to follow their base instincts, but he does seem to have underestimated the potential for this to happen in the absence of traditional social norms.