Why does NIST want 112-bit security from 128-bit key size for lightweight cryptography?
From the security perspective, they should require 128-security.

Why?
NIST has a requirement for a minimum security strength of 112 bits for all things cryptographic, at least for the present.  You see it everywhere in their documents.  For example, in Transitioning the Use of Cryptographic Algorithms and
Key Lengths it says

For the Federal Government, a security strength of at least 112 bits
is required at this time for applying cryptographic protection (e.g.,
for encrypting or signing data). Note that prior to 2014, a security
strength of at least 80 bits was required for applying these
protections, and the transitions in this document reflect this change
to a required security strength of at least 112 bits.

Apparently, the cryptographers at NIST believe that 112 bits of security is sufficient for now.  128 bits is coming though.

SP 800-57, Part 1 includes a transition to a security strength of 128
bits in 2030; in some cases, the transition would be addressed by an
increase in key sizes.

Do note that this is their minimum requirement for the US Federal government, your requirements may be different.