How do these triplets code for these proteins?
In the first image, AAG is the true codon for Lysine.  So when the ribosome hits "AAG" in the mRNA it recruits a Lysine-tRNA.  

What can be confusing is the use of the term "coding strand" when talking about the DNA. The coding strand is illustrated in the second image you posted, and it is the coding strand of DNA that the first image is depicting. What "coding strand" means here is, this is the strand that looks like the mRNA will look. Depicting the DNA coding strand like this--i.e. as a series of codons--can be slightly misleading since we know codons really only mean anything when in the form of mRNA. Nevertheless, it is a common way of thinking about DNA.

Back to the first image. Because it is showing the "coding strand" of DNA, the "template strand" for 5'-AAG-3' then must be 5'-CTT-3'. Hence, when this strand is transcribed by RNA polymerase, the 5'-CTT-3'(DNA) becomes 5'-AAG-3'(mRNA).