[By thy life] is an oath. [They are indeed in their intoxication] means: in their misguidance. [Wandering blindly] means: they are confused.
Muhammad said: The words al-'umr and al-'amr, according to the linguistic scholars, carry the same meaning. When it is used in an oath, the first letter is vocalized with a fatha (vowel sign 'a') due to its frequent usage, because the fatha is lighter [to pronounce].
﴿لعمرك﴾ قسمٌ ﴿إِنَّهُم لفي سكرتهم﴾ يَعْنِي: ضلالتهم ﴿يعمهون﴾ يَتَحَيَّرُونَ.
قَالَ محمدٌ: الْعَمْرُ وَالْعُمْرُ عِنْدَ أَهْلِ اللُّغَةِ بِمَعْنَى واحدٍ؛ فَإِذَا اسْتُعْمِلَ فِي الْقَسَمِ فُتِحَ أَوَّلُهُ؛ لِكَثْرَةِ اسْتِعْمَالِهِمْ لَهُ؛ لأَنَّ الْفَتْح أخف.