I'm assuming the OP concerns chemical means of modifying residues. Multiple protein residues other than Lysine may be labeled with an adduct. Here are some examples:
Histidine residues may be labeled using an epoxide attached to a ligand. (Chen et al., 2003)
Cysteine residues may be labeled with a nitrile derivative where the sulhydryl acts as the nucleophile. (Obella et al., 2007)
Arginine residues may labeled using a derivative of the naturally occurring methylglyoxal. (Oya et al., 1999)
Carboxylate functionality such as in Aspartate and Glutamate residues as well as the C-terminus may be labeled via the formation of an amide linker using a carbodiimide such as N-ethyl-3-N',N'-dimethylaminopropylcarbodiimide (EDC). (Gilles et al., 1999)
The above list of residues is not comprehensive, nor are the labeling agents. I recommend checking out the reviews by Basle et al. (2010) and Chen and Wu (2016).
References
Basle, E, Joubert, N, Pucheault, M (2010) "Protein Chemical Modification on Endogenous Amino Acids" Chemistry & Biology 17:213-227. DOI: 10.1016/j.chembiol.2010.02.008
Chen, X and Wu, Y-W (2016) "Selective chemical labeling of proteins" Org. Biomol. Chem. 14:5417-5439. DOI: 10.1039/C6OB00126B
Gilles, MA, Hudson, AQ, Borders, CL (1990) "Stability of water-soluble carbodiimides in aqueous solution" Anal. Biochem. 184:244-248. DOI: 10.1016/0003-2697(90)90675-Y
Gong Chen, Alexander Heim, Doris Riether, Dominic Yee, Yelena Milgrom, Mary Ann Gawinowicz, and Dalibor Sames (2003) "Reactivity of Functional Groups on the Protein Surface: Development of Epoxide Probes for Protein Labeling" J. Am. Chem. Soc. 125:8130–8133. DOI: 10.1021/ja034287m
Oballa, RM, Truchon, JF, Bayly, CI, Chauret, N, Day, S, Crane, S, et al. (2007) "A generally applicable method for assessing the electrophilicity and reactivity of diverse nitrile-containing compounds" Bioorg. Med. Chem. Lett. 17:998–1002. DOI: 10.1016/j.bmcl.2006.11.044
Oya, T, Hattori, N, Mizuno, Y, Miyata, S, Maeda, S, Osawa, T, Uchida, K (1999) "Methylglyoxal modification of protein. Chemical and immunochemical characterization of methylglyoxal-arginine adducts" J. Biol. Chem. 274:18492-18502. DOI: 10.1074/jbc.274.26.18492