Take a look to this paper. They measure aminoacids in LB by HPLC. However I am afraid that the real concentration will depend from batch to batch since it is a complex medium.
Silivia, some companies like DIFCO do maintain the quality standards of the tryptone and Yeast extract which are thr prime ingredients of LB. Following is the sheet attached for your reference which gives the individual aminoacids present in Tryptone and yeast extract