The determining factor in Robert Ferrar's ability to marry Lucy Steele without his mother's intervention is not suitability. The determining factor is wealth. Mrs. Ferrars took an action that liberated Robert and gave him full discretion in his decisions.
When Mrs. Ferraras was so very, very outraged over the news that Edward was not only engaged to Lucy but fully intended to honor the engagement and marry Lucy, Mrs. Ferrars called in her lawyers. Mrs. Ferrars ordered her lawyers to rewrite her will irrevocably cutting Edward out of inheritance. But she did more than that. Mrs. Ferrars also ordered her lawyers to irrevocably fix all her wealth and property on Robert. This means that Robert has full authority to use all the family wealth without any restraints attached.
In other words, Robert doesn't need Mrs. Ferrars permission for anything ever again. One reason Edward was being so cautious about Lucy was because he needed Mrs. Ferrars blessing and permission to marry so that he would not get cut out of her will and be penniless and careerless. Robert no longer has any problem of the sort and so could marry Lucy if he wanted to--and she convinced him that he did want to!
Austen doesn't introduce this scenario into the story as a trivial plot device. It is an important part of her examination of the relationship between wealth and marital choice and happiness. It contrasts, for instance, to the relationship relevant to Willoughby's marital situation regarding Miss Sophie Grey, who has an independent fortune. Willoughby is marrying her for her wealth (and because she is beautiful...). He needs her wealth to live the kind of life he desires. He has no wealth in his own right and the one relative who provided for him, Miss Smith, is angry with him and not forthcoming with his promised wealth.
The dynamic between Willoughby and Miss Grey that contrasts to the Robret Ferrars-Lucy situation is that until they are married, Miss Grey controls her money and uses it to force Willoughby to do what she wants him to do. The similarity of the two cases is taht both Robert Ferrars and Sophie Grey have independent wealth and can use it to manipulate marital advantage.
By developing these scenarios Austen is showing that in England women were bound by what they could or could not provide in terms of wealth and that men could also be manipulated and controlled by the people who held the wealth. Therefore men's choices could be as limited and restricted as women's when the men themselves didn't have independent wealth (she touches on this also in Pride and Prejudice in the person of Darcy's cousin Fitzwilliam).