The 1905 LDS edition here omitted the definite article the from the archaic phrase “at the last” (which means ‘in the end’). The 1920 LDS edition restored the the to the LDS text. Elsewhere in the Book of Mormon, there are two instances of “at last” without the the:
Both of these instances of “at last” mean ‘in the end’.
There is one other instance of “at the last” in the text, but it does not mean ‘in the end’; instead, “begin at the last” refers to trees and means ‘begin with the last trees’:
One might propose that in Alma 5:59 the unique instance of “at the last” (with its meaning ‘in the end’) could be the result of some error in the early transmission of the text. Note the high frequency in the text of the longer phrase “at the last day” (49 times), which could have led the scribe to accidentally write “at the last” in Alma 5:59 rather than “at last”.
In the King James Bible, there are occurrences of the phrase “at the last” with the meaning ‘in the end’, as in these two examples:
The Oxford English Dictionary lists “at the last” as a variant of “at last” (see definition 10a under the sixth listed noun last), with citations of “at the last” dating from about 1275 to 1821. Thus the unique occurrence of “at the last” in Alma 5:59 is clearly possible. The critical text will accept this now archaic reading “at the last”.
Summary: Maintain in Alma 5:59 the archaic phrase “at the last” (which means ‘in the end’); both “at the last” and “at last” are found in the Book of Mormon text.