Which analysis of خَرَجْتُ مِنَ الْفَصْلِ لِأَشْرَبَ الْمَاءَ is correct?

Kay, Idhan, Hatta and Purpose Li

• لِأَشْرَبَ gives the purpose of leaving, and the verb ends in fatḥah
• لِ marks the person who left
• أَشْرَبَ is a past-tense verb
• The sentence expresses only an endpoint