If she had her fallopian tubes tied, is it permissible for her to ask Allah to bless her with a son?

The basic principle is that tying the fallopian tubes prevents pregnancy except in the event of a medical error, such as not tying them properly. You can find out whether the tubes are open or blocked by doing a salpingogram (X-ray with a contrast dye inserted into the uterus and fallopian tubes), as a specialist doctor advised us.

If the fallopian tubes are open, then it is possible to get pregnant, and we ask Allah to bless you with a righteous son.

If the fallopian tubes are blocked, then usually it is not possible to get pregnant, and in that case praying for that is overstepping the line. So you should be patient and praise Allah for the daughters with whom He has blessed you, for how many women there are who have not been blessed with either daughters or sons. Allah, may He be exalted, says (interpretation of the meaning):

{To Allah belongs the dominion of the heavens and the earth; He creates what he wills. He gives to whom He wills female [children], and He gives to whom He wills males

Or He makes them [both] males and females, and He renders whom He wills barren. Indeed, He is Knowing and Competent} [ash-Shoora 42:49-50].

Daughters are a great blessing, for that is what Allah chose for His Prophet (blessings and peace of Allah be upon him).

Having daughters is a blessing of which many people are unaware, for they are easy to raise, very responsive and there is a great reward for treating them kindly, as the Prophet (blessings and peace of Allah be upon him) said: “Whoever takes care of two girls, he and I will enter Paradise like these two” – and he held his fingers together. Narrated by Muslim (2631).

According to a report narrated by at-Tirmidhi (1914): “Whoever takes care of two girls, he and I will enter Paradise like these two” – and he gestured with his two fingers. Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.

We have noted previously in the answer to question no. 307589 that praying for something which is ordinarily impossible is overstepping the mark and is prohibited.

But if you have not done the salpingogram and you are not certain that the tubes are blocked, then it is permissible to ask Allah, may He be exalted, for a righteous son, because that is possible even if the possibility is slight.

And Allah knows best.