If a widow does not want to get married, can she fall in love with a married person who will take care of her sexual needs? In the past this was the duty of the deceased siblings. How should they go about enjoying life?
Having a relationship with a man married to someone else is called adultery. You cannot be involved in adultery and be a Christian. "Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived. Neither fornicators, nor idolaters, nor adulterers, nor homosexuals, nor sodomites, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners will inherit the kingdom of God" (I Corinthians 6:9-10). In what you propose you are not only sinning against God, you are also helping to ruin another marriage.
Under the law of Moses, the wife of a man who died without children was married to the nearest of kin. The first child that they had would be considered the child of the man who died and that child would inherit the man's estate. "If brothers dwell together, and one of them dies and has no son, the widow of the dead man shall not be married to a stranger outside the family; her husband's brother shall go in to her, take her as his wife, and perform the duty of a husband's brother to her. And it shall be that the firstborn son which she bears will succeed to the name of his dead brother, that his name may not be blotted out of Israel" (Deuteronomy 25:5-6). We do not live under the law of Moses. It came to an end when Jesus died on the cross (Colossians 2:14). But notice that what you wish to do would be considered sinful under that law anyway since you do not wish to marry and the man you are involved with is not a relative anyway.
The rule for Christians widows is to marry again if she is still interested in sexual relations and a family. "Therefore I desire that the younger widows marry, bear children, manage the house, give no opportunity to the adversary to speak reproachfully" (I Timothy 5:14).