X ни в чём себе не отказывает - X denies himself nothing
X does not refuse himself anything
X spares no expense to gratify his fancies (desires etc)
(in limited contexts) X doesn't have to deny (to refuse) himself anything.
Там у ней (Одинцовой) был великолепный, отлично убранный дом, прекрасный сад с оранжереями: покойный Одинцов ни в чём себе не отказывал (Тургенев 2). There she (Mme Odin-tsov) was mistress of a magnificent, excellently appointed house with a beautiful garden and conservatories: the late Odintsov had denied himself nothing (2e). There she (Mme Odintsov) had a magnificent, splendidly furnished house and a beautiful garden, with conservatories, her late husband had spared no expense to gratify his fancies (2b).
...Губернские дамы... всё-таки были не более как чиновницы, какие-нибудь председательши, командирши и советницы, родившиеся и воспитывавшиеся в четвёртых этажах петербургских казённых домов и только недавно, очень недавно, получившие понятие о комфорте и о том, что такое значит «ни в чём себе не отказывать» (Салтыков-Щедрин 2). ...Our provincial ladies...were after all only the wives and daughters of civil servants, a wife of some departmental president or of the commanding officer of the local garrison or of some councillor, all born and educated on some fourth story of a Petersburg government building, who had obtained their ideas of comfort only very recently, since it was only quite recently that they had really understood the meaning of the phrase, "not to have to deny oneself anything" (2a).
Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. С.И. Лубенская. 2004.