. . . at last [ət-lӕst] . . [audio source]
I guess, from the two lots’ pronunciations, that when [ӕ] is accompanied by [ӕ], one which is lesser important in meaning becomes weaker and change into a schwa sound. Is this a typical pattern?
The change in the vowel in at last has nothing to do with the fact that two open-front vowels are near each other. Nobody weakens the vowels in rat trap, another phrase with two /ӕ/ vowels. The reason the vowel is weakened in at last is that the word at is unstressed.
Vowels in unstressed syllables in English are often reduced, meaning they change into a /ə/. In the phrase at last, and in many similar phrases (at odds, at most, at least), the word at is unstressed, and the vowel tends to be reduced to /ə/. You can see that in at odds and at most, the two vowels are not both open front; yet the vowel in at is still weakened.