Does supplicating with the formula, "O Lord, I ask You to cure me by the number of Your creation, the pleasure of Your Self, the weight of Your Throne, and the extent of Your words," count as a lie if said once? And is saying this formula after any supplication or remembrance a correct ijtihad, or a lie that leads to sins?

What you mentioned is not a lie, whether in dhikr (remembrance) or du'a (supplication), even if you did not repeat the words the specified number of times. This is because what you did is merely a reference to a reality, asking Allah Almighty to grant you according to its number. The Sunnah and the sayings of scholars contain evidence for the permissibility of this, such as the hadith of Juwayriyah (may Allah be pleased with her), where the Prophet (peace and blessings be upon him) said: "Subhan Allah wa bihamdihi adada khalqihi, wa rida nafsihi, wa zinata arshihi, wa midada kalimatihi" (Glory be to Allah and praise be to Him, as many as His creation, as much as pleases Him, as much as the weight of His Throne, and as much as the ink of His words). And like the saying of Ash-Shafi'i: "May Allah's blessings be upon our Prophet whenever those who remember Him remember Him, and whenever those who are heedless of Him are heedless of His remembrance." And the saying of Ibn Allan: "As many as His creation, as much as pleases Him, as much as the weight of His Throne, and as much as the ink of His words, whenever a rememberer remembers Him, and whenever a heedless person is heedless of His remembrance." Ash-Shawkani said: Dhikr multiplies and increases by referencing its number, even if the dhikr itself is not repeated.