I am a Muslim and have one sister who is a non believer, she worships Gea, a mythological entity. Is it haraam for me to make Dua and ask forgiveness for her. I have read some hadith on the subject but they refer to deceased parents, my sister is still alive.
If they are known mushrik then you cannot pray for their forgiveness.
مَا كَانَ لِلنَّبِيِّ وَالَّذِينَ آمَنُوا أَن يَسْتَغْفِرُوا لِلْمُشْرِكِينَ وَلَوْ كَانُوا أُولِي قُرْبَىٰ مِن بَعْدِ مَا تَبَيَّنَ لَهُمْ أَنَّهُمْ أَصْحَابُ الْجَحِيمِ
It is not for the Prophet and those who have believed to ask forgiveness for the polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire.
There is no mention of whether you can pray for guidance (not forgiveness) for mushrik though. However if they are not mushrik, merely kaffe, then you may pray for guidance or forgiveness. It is a good deed to pray for other's guidance.
Allah guides whom he wills.
أَفَمَن زُيِّنَ لَهُ سُوءُ عَمَلِهِ فَرَآهُ حَسَنًا ۖ فَإِنَّ اللَّهَ يُضِلُّ مَن يَشَاءُ وَيَهْدِي مَن يَشَاءُ ۖ فَلَا تَذْهَبْ نَفْسُكَ عَلَيْهِمْ حَسَرَاتٍ ۚ إِنَّ اللَّهَ عَلِيمٌ بِمَا يَصْنَعُونَ
Then is one to whom the evil of his deed has been made attractive so he considers it good [like one rightly guided]? For indeed, Allah sends astray whom He wills and guides whom He wills. So do not let yourself perish over them in regret. Indeed, Allah is Knowing of what they do.