Okay, so melamine is not detected as protein in Lowry method. That clears up one issue, thank you.
What I understand so far about the Lowry method is this - the copper ions form a complex with 4-6 peptide bond nitrogens. This is the Biuret reaction. Then an electron is transferred from the complex to the Folin-Ciocalteau reagent (i.e. phosphomolybdic acid-phosphotungstinic acid complex). That electron reduces the Folin-Ciocalteau reagent and causes blue color. Additionally cysteine, tryptophan and specially tyrosine can act as reducing agent (due to side chain or something, I am not sure) and can cause blue color formation independently.
Now this explanation would fit if copper ion in the peptide-copper complex was in the cuprous form. Then the cuprous ion could give an electron to the Folin-Ciocalteau reagent and become cupric ion. So the question is whether the complex formed in Biuret reaction contain cupric ion or cuprous ion.
Since the reagent used for Biuret reaction is basically the Fehling reagent, I am considering that before the Biuret reaction takes place there is cupric ion-tartrate complex. Then the peptide bonds will react with the cupric ion. So, is the complex formed cuprous-peptide complex or cupric-peptide complex? (sorry for the repeat)
Of course, some internet references are saying that Tyr, Trp, Cys are the ones responsible for blue color in Lowry method. Others are saying that the copper-peptide complex is essential for blue color formation. I believe the latter because otherwise there is no need to use the Biuret reaction, we could do this just by Folin-Ciocalteau reagent.
Summery: The reactions taking place in Lowry protein assay method are poorly understood (by me).