No, at least so far as the law is concerned. But after its initial publication in 1928, it was not until the 1960s that litigation in the US and the UK allowed it to become generally available. An op-ed by Fred Kaplan in the today’s New York Times, entitled The Day Obscenity Became Art, (with added links) tells us that

today is the 50th anniversary of the court ruling that overturned America’s obscenity laws, setting off an explosion of free speech — … The historic case began on May 15, 1959, when Barney Rosset, the publisher of Grove Press, sued the Post Office for confiscating copies of the uncensored version of D. H. Lawrence’s 1928 novel “Lady Chatterley’s Lover,” which had long been banned for its graphic sex scenes.

… Mr. Rosset hired a lawyer named Charles Rembar, … [who] presented “Lady Chatterley” as a novel of ideas that inveighed against sex without love, the mechanization of industrial life and morbid hypocrisy. … On July 21, 1959, Judge Bryan ruled in favor of Grove Press and ordered the Post Office to lift all restrictions on sending copies of “Lady Chatterley’s Lover” through the mail.

That case was Grove Press v Christenberry 175 F.Supp. 488 (S.D.N.Y., 1959); it was upheld on appeal (at 276 F.2d 433 (2nd Cir., 1960) (Justitia | OpenJurist); and Robert McHenry on Britannica blog has also entertainingly marked the anniversary.

Rembar wrote about his experiences defending this book and other controversial novels in The end of obscenity; the trials of Lady Chatterley, Tropic of Cancer, and Fanny Hill (New York, Random House, 1968): Tropic of Cancer reached the Supreme Court in Grove Press v Gerstein 378 US 577 (1964), and Fanny Hill reached the same court in Memoirs v Massachusetts 383 US 413 (1966).

When these cases were decided, the leading US Supreme Court decision on obscenity was the relatively conservative Roth v US 354 US 476 (1957), and these cases were decided within its confines: the value of Grove Press v Christenberry was that it demonstrated that the Roth standard did not preclude First Amendment protection to obscene speech, at least where that speech embodied ideas of redeeming social importance. It laid the foundations for cases like Grove Press v Gerstein, Jacobellis v Ohio 378 US 184 (1964) and Memoirs v Massachusetts. These, in turn, led to the far more progressive stance taken by the Supreme Court in Miller v California 413 US 15 (1973), which held that a work is obscene and can be regulated by a State where that work, taken as a whole, appeals to the prurient interest in sex; portrays, in a patently offensive way, sexual conduct specifically defined by the applicable state law; and, taken as a whole, does not have serious literary, artistic, political, or scientific value. The plaudits probably belong to all of these cases, and not merely to Grove Press v Christenberry, but it is still an important and entertaining case for all that.

Moreover, Lady Chatterley’s Lover had also been the basis for a contemporary challenge to the UK’s Obscene Publications Act, 1959. It is an infamous trial, from the prosecution’s notorious and patronising rhetorical demand of the jury whether it was something they would want their wives or servants to read, to the cast of literary worthies who testified to the novel’s worth, to the jury’s acquittal on 2 November 1960. The following day, Penguin sold its entire first print run of 200,000 copies, and sold 2 million copies in six weeks. The Times has a wonderful collection of archive material about the case, the full papers from the trial are now available at Bristol University Library; Penguin have recently re-issued their classic account of the trial; and the BBC have made a marvellous drama (BBC | imdb | Times) of two fictional jurors’ experience.

These were undoubtedly important developments, but I can’t help but fear that the days of such trials might come back again.