Wiktionary
n. A male-female marriage entered into in the hope of concealing the non-heterosexual sexual orientation of one or both of the spouses.
Wikipedia
Lavender marriage is the popular term used to describe a male-female marriage in which one or both of the partners was homosexual–or possibly bisexual. The more general term is mixed-orientation marriage. It is a specialized instance of a marriage of convenience, in which the marriage is formed for some reason other than the romantic attachment assumed to be the basis of modern marriages, for legal reasons involving inheritance or immigration, for example.
The partners in a lavender marriage were concealing the fact that the sexual orientation of at least one of them was not primarily heterosexual. The term lavender marriage dates from the early twentieth century and is used almost exclusively to characterize certain marriages of public celebrities in the first half of the twentieth century, primarily before World War II. At the time, public attitudes toward homosexuality made it impossible for a person to pursue a public career, notably in the Hollywood film industry, while acknowledging homosexuality. One of the earliest uses of the phrase appeared in the British press in 1895 when lavender was associated with homosexuality.