If you feel comfortable reading Japanese, I think this article can explain it fairly well 「せめて」と「少なくとも」の違いとは？分かりやすく解釈 | 言葉の違いが分かる読み物. Either way, I’ll kind of summarize what I got from the article, first starting with the “general” definitions it gives for the two:
From my understanding, it looks like 少なくとも is used with a numerical value, or a “degree” of some sort indicating the lowest it can/should go. Additionally, it’s also used when someone should be doing something at the very minimum. On the other hand, せめて is used when you’re unsatisfied with a certain situation and are expecting something to the minimum degree of where you’ll be satisfied (such as - you got 5 dollars, but you wanted at least 10 dollars). You’ll notice that uses a numerical value, but the overall idea here is that there was dissatisfaction with receiving 5 dollars when there was an expectation of receiving a minimum of 10. While on the other hand, 少なくとも would be used in an example such as “I think I can lose at least 5 pounds” or “It will take at least half a year before it’s complete”.