[noun] + でよければ [na-adj] + でよければ
でよければ offers something modestly: "if X will do", "if X is all right with you". It follows a noun – yourself, a thing, a time – and the second half says what you will do. It is でいい, "X will do", in the ば-form.
Offering yourself, わたくし私でよければ, is the commonest use: you may not be the best person for it, but you're willing.
In formal speech and in business, でよろしければ takes the place of でよければ. Without a noun, よろしければ is the polite "if you like".