A quick word of advice, I like to test scripts out in the Scripting Index. I went to the Files In Directory example and substituted your values. If you want to just have one for loop, you'll need to ensure that your lst1 has the exact match. But for this example, you need a nested for loop. You also need to switch the Contains arguments from lst1, filelist[i] to filelist[i], lst[j].
filelist = {"123_123_1_acdr.csv", "234_113_100_rqtfgy.csv",
"53_1243_12_qqwed.csv", "6_12378_23_rty.csv"};
lst1 = {"234_113_100"};
lst2 = {};
For( i = 1, i <= N Items( filelist ), i++,
For(j = 1, j <= N Items(lst1), j++,
If( Contains( filelist[i], lst1[j] ),
Insert Into( lst2, filelist[i] )
)
)
);
Print( lst2 );
Result: {"234_113_100_rqtfgy.csv"}