Does my case of slight lisp in pronouncing the letter "ra" as "ghayn" exempt me, especially in Surat Al-Fatiha, given that attempting to correct it causes hardship and leads to missing following the Imam? And what is the limit of pronunciation that does not change the meaning?

As long as you are afflicted by waswasah (whispers/obsessive thoughts), you must disregard and ignore these whispers and doubts. If you doubt the correctness of pronouncing any letter, do not pay attention to it and proceed with your recitation, because this is the effective cure for waswasah. Know that the prayer of a person with a lisp is valid for himself if he cannot learn to correct it, unlike someone who can, for whom correcting the pronunciation is necessary. As for a slight lisp, it does not harm at all. It is stated in Hashiyat Ibn Abidin, Asna al-Matalib, Hashiyat al-Rawd al-Murabbi’, and Al-Insaf that a slight lisp that does not prevent the original articulation point or that does not produce the letter clearly does not affect the prayer. Based on this, you should not repeat words about whose pronunciation you have doubts, because it is merely waswasah. And if there is something slight of that, it does not harm.