This Germanic word is known from Anglo-Saxon times, where it meant "lay" (as opposed to "clerical") and later "unlearned". It developed several new senses in the 14th century, but only the sexual meaning survives today.
That sense turns up just once in Shakespeare, when Buckingham tells the Mayor of London that Richard is not someone to be found "lulling on a lewd love-bed" (Richard III, III.vii.71).
In all other cases, it is important to avoid the sexual connotations. So, when Petruchio tells a haberdasher that a cap is "lewd and filthy" (The Taming of the Shrew, IV.iii.65), he means "cheap and nasty" And when Poins tells Prince Henry "you have been so lewd" (Henry IV Part 2, II.ii.58) he means only "improper, unseemly".
The word can mean "wicked, evil", as when Leonato describes Borachio as a "lewd fellow" (Much Ado About Nothing, V.i.317), and when Richard complains of people troubling King Edward with "lewd complaints" (Richard III, I.iii.l61). he means "ignorant, foolish".