Λ-11 spent most of her waking moments trapped in a tube, being poked and prodded and otherwise tortured in the name of science by faceless doctors, but she had no mouth with which to voice her cries of pain. The only thing really known was that Relius Clover had built her at some point in the past, but apparently the scientists involved decided she was too obsolete and moved on.
After v-13 (pronounced 'Nu-13') was defeated by Ragna the Bloodedge, Kokonoe wanted a copy of the unstoppable killing machine, but at the same time she was afraid of accidentally bringing back the insane personality with it. Kokonoe found a solution by sending Tager to fetch Lambda's body from the rubble of a dead city, then placed the "soul" of the broken v-13 in the body of Λ-11. At the same time, she stripped Lambda of her personality and memories, making it completely loyal puppet.
Kokonoe hopes to use Lambda to find and capture Noel and possibly even defeat Terumi, but who knows how the soul of v-13 might end up affecting the unit?