Mr. Lucas, a Viennese-born London correspondent, has written a firm and sobersided biography of the Lawrences -- in fact D. H. (and his work) takes precedence over Frieda as he never did in life. Lucas' account, the first in some years, adds little while it subdues, certainly in tone, much that appeared right after Lawrence died. The story remains just as we remember it -- that of the essentially weak, febrile, mother-dominated young man (""Nobody can have the soul of me. My mother has had it. . ."") who met Frieda when she was restively married to Ernest Weekley, a professor in Nottingham. Impulsive, attractive, untidy but always spirited, Frieda stayed with Lawrence until his death (except for a short, occasional side-trip) in spite of their violent flare-ups centering around her regrets for the three children she'd forfeited and his failure to subjugate her. They endured the ""scandalous persecution"" of the war years in England where they were ""buried. . . like toads under a mushroom,"" and then resumed their continental travels here and there as well before the sojourns in Taos and Mexico. This is a work of considered probity and since the Lawrences knew -- it would seem -- all their artist-writer contemporaries, Lucas has provided convenient eyedropper summaries of them en route. Unfortunately Frieda and Lawrence remain far more alive in their own words or those of their friends than those of Lucas who is staid, perhaps in his attempt to be scrupulous: ""What can one say about Frieda's behavior at this time? It is not necessary to seek excuses for her: the biographer's task is not to pass judgments but to present the facts as they are. . . ."" The facts are here but what of the numen (the word Huxley applied to Lawrence) or more simply the headlong vitality Frieda apotheosized?