The condition for an oath to be binding is that the person who swears must do it so verbally i.e. by moving his tongue.
If he does not speak of it and he does not move his tongue in order to do so, then the oath is not binding. Because of the general meaning of the words of the Prophet (blessings and peace of Allah be upon him): “Verily Allah has pardoned my ummah for what crosses their minds, so long as they do not do it or speak of it.”
Qataadah said: If the word of divorce crosses his mind, then it does not mean anything.
Narrated by al-Bukhaari (5269)
If a person does not speak of oath and does not swear rather it is something that just crosses his mind then this does not have any impact, and no consequences result from it, neither sin nor expiation.
Moving the lips is more significant than moving the tongue, because moving them can hardly happen except by moving the tongue.
Imam Ahmad narrated in his Musnad (10968) from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “Verily Allah, may He be glorified and exalted, said: ‘I am with My slave when he remembers Me and moves his lips in mention of Me.’” Classed as saheeh by al-Albaani and the commentators on al-Musnad.
Imam al-Bukhaari (may Allah have mercy on him) compiled a chapter on the verse: “Move not your tongue concerning (the Quran, O Muhammad (blessings and peace of Allah be upon him)) to make haste therewith” [al-Qiyaamah 75:16], and quoted this hadith qudsi in the chapter.
This indicates that moving the lips implies moving the tongue, and there is a greater emphasis on mentioning Allah. Based on the above evidence, if a person speaks out loud and moves his tongue while swearing then the oath is binding and the person has to fulfil it. If unable to fulfil or broke it then he is supposed to offer expiation.
And Allah knows best