Involved in both the arginine and lysine biosynthetic pathways. Phosphorylates the LysW-bound precursors glutamate (for arginine biosynthesis), respectively alpha-aminoadipate (for lysine biosynthesis). [amino-group carrier protein]-C-terminal-N-(1,4-dicarboxybutan-1-yl)-L-glutamine + ATP = [amino-group carrier protein]-C-terminal-N-(1-carboxy-5-phosphooxy-5-oxopentan-1-yl)-L-glutamine + ADP [amino-group carrier protein]-C-terminal-gamma-(L-glutamyl)-L-glutamate + ATP = [amino-group carrier protein]-C-terminal-gamma-(5-phospho-L-glutamyl)-L-glutamate + ADP Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-lysine from L-alpha-aminoadipate (Thermus route): step 2/5. Amino-acid biosynthesis; L-arginine biosynthesis. Belongs to the acetylglutamate kinase family. LysZ subfamily.