If a person does not want to tell how much his monthly income is to some outsider, but the outsider persistently asks about it, is it alright for the particular individual to lie about it because he fears that the outsider would spread it around?

Lying is haraam but what you can do is to tell the person that you cannot disclose the salary because of confidentiality. You can tell them that knowing your salary does not matter to him. You should remind the person of the hadeeth that says, "It is from the excellence of a person's Islam to shun that which does not concern him." [1]

Reference:

[1] At-Tirmidhi  Book 1, Hadith 67