Praise be to Allah.
The word “Allahumma” is a kind of call, like saying “Ya Allah (O Allah),” as in the verse in which Allah, may He be exalted, says (interpretation of the meaning):
“Say, ‘O Allah [Allahumma], Owner of Sovereignty…’”
[Aal ‘Imraan 3:26].
At-Tabari (may Allah have mercy on him) said:
With regard to the meaning of the phrase “Say, ‘O Allah [Allahumma]”, what is meant is: “Say, O Muhammad: O Allah…”.
End quote from Tafseer at-Tabari (5/299).
Mentioning the name of Allah with this phrase, “la hasad (no jealousy)” may mean one of two things:
- Asking Allah to bear witness that the heart is free of jealousy.
In other words (one is saying): O Allah, I ask You to bear witness that there is no jealousy in my heart towards the person of whom I am speaking, or: O Allah, You know that there is no jealousy that is prompting me to say what I am saying about him, and the like.
This kind of asking Allah to bear witness is permissible, if it is true and if the speaker knows in his heart that there is no lie involved in this calling upon Allah to bear witness. If it is a lie, then it is a grave sin. Please see the answer to question no. 218835.
- Or the meaning could be something along the following lines: O Allah, do not leave in my heart any jealousy towards this person, and the like.
This meaning is also permissible, and there is nothing wrong with it, because supplication for warding off evil is prescribed in all circumstances.
For more information, see the answer to question no. 198616.
And Allah knows best.