It does not has a 'K' in its name. It does not have a potassium in its chemical composition.
Would be nice to know why Glutamine is Q too, some of these abbreviation seems simply random.
From here
Back in 1960's Dr.Dayhoff was shortening the names of amino acids so that ancient computers could save computing time.
By the time Dr. Dayhoff got to lysine, there were not too many letters left, so she used the letter K, explaining that K is at least near L in the alphabet.
As for Glutamine.
For the remaining 5 amino acids, Dr. Dayhoff was reaching somewhat to find an easy-to-remember connection between the single letter and the amino acid. She assigned aspartic acid, asparagine, glutamic acid and glutamine the letters D, N, E and Q, respectively, noting that D and N are nearer the beginning of the alphabet than E and Q, and that Asp is smaller than Glu, while Asn is smaller than Gln.
Šorm et al. were the first to publish a specific single letter abbreviation system, in On proteins. LXIII. Lower structures in the chains of proteins Collect. Czech. Chem. Commun. 1961, 26, 531-578.
In this publication, an earlier, previously unpublished, system of Hans Neurath was also published.
If practical symbols are to be proposed, they must conform to the following requirements: (l) 23 different one-letter symbols of amino acids occurring in protein structures have to be chosen, (2) only simple symbols currently accessible in printing-works with the possibility to be written by common typewriters have to be used, (3) the symbols must offer the possibility of expressing whether the bond of the sequence is determined or, alternatively, so far undetermined, within the space of one single letter, and (4) the usage of symbols must be of international applicability.
The usage of figures is excluded by requirement (1), and the usage of Greek or other uncommon letters and symbols by requirement (2). The most appropriate manner seems to be the use of the common letters of the Latin alphabet, which conforms to requirement (4) and permits to distinguish according to (3) between determined and undetermined sequences by choosing either capital or small letters. To express a determined sequence of the peptide chain we propose to use capital letters according to Table VIII, and, further, to put small letters at places where brackets and commas have hitherto been used. Our symbols are derived from the English names of amino acids. Since, however, identical letters commonly recur at the beginning of the names they could not be consistently utilized in our symbols. Nor could a thorough system be compiled involving two-letter symbols of the first two letters of the name (e. g. glutamic acid, glutamine, glycine); moreover this would be contradictory to the intended system of one-letter symbols. Therefore, we have compromised and the first letters are proposed as symbols only in some instances (asparatic acid, glutamic acid, cystine (half-), histidine, methionine, proline, serine, tryptophan, valine), in many other cases characteristic symbols derived either from the spelling (ala- l, arg- r, lys- i, leu- u, ileu- w, phe- f) or from the graphical representation (glu- g, glu(NH$_2$)- q) were chosen.
Šorm was the first to use "Q" for glutamine. (Neurath had used "E' for both glutamine and glutamic acid.)
Neurath used "O" for lysine and Šorm used "I".
No one unified system was used until selection by IUPAC.