Lufthansa won't make a fuss, the ID is not verified for infants. The agent must have added the infant to the mother during the booking process so it shows with the last name of that passenger. No worries at all.
In Amadeus the first name of the infant shows in the reservation. The last name of the pax it is associated to if pulled, but not mission critical
Code:
CREATE NAME ELEMENT EN 21APR22 0714Z
PASSENGER WITH INFANT
---------------------
THERE IS A SPECIAL PASSENGER TYPE CODE (INF) FOR INFANTS
TRAVELING WITH AN ADULT PASSENGER. THIS TYPE CODE IS
EXCEPTIONAL AS IT IS ENTERED WITH THE ACCOMPANYING ADULT
PASSENGER.THE DATE OF BIRTH (DOB) OF INF/CHD MUST ALWAYS BE
INCLUDED.
ENTER FOR EXAMPLE:
NM1LEAVEY/PATRICK(INF/MICHAEL/01JUN21)
NM TRANSACTION CODE
1 NUMBER OF PASSENGERS WITH THIS SURNAME, WHO
ARE OCCUPYING SEATS
LEAVEY/PATRICK PASSENGER SURNAME, SLASH, GIVEN NAME
( OPEN BRACKET, DELIMITER FOR THE PTC
INF CODE FOR INFANT PTC
/ SLASH, DELIMITER, MANDATORY IF THE NAME OR
DOB IS INCLUDED
MICHAEL INFANT'S GIVEN NAME (OPTIONAL)
/01JUN21 SLASH, INFANT'S AGE AT TIME OF TRAVEL, DATE
) OF BIRTH OBLIGATORY, CLOSE BRACKET
SYSTEM RESPONSE:
1.LEAVEY/PATRICK(INFT/MICHAEL/01JUN21)
2 OK 654 Y 18SEP 2 PRGSTN HK1 N1 0730 0830 319 EOS
SEE RTSVC
3 SSR INFT OK NN1 LEAVEY/MICHAEL 01JUN21/S2
IF THE INFANT'S SURNAME DIFFERS FROM THE NAME OF THE ADULT,
ENTER THE SURNAME IMMEDIATELY AFTER INF, FOR EXAMPLE:
NM1BROWN/ANNE(INFBIGG/HANNAH/10JUN21)
NOTE: IT IS NOT POSSIBLE TO ENTER THE INFANT'S SURNAME WITHOUT
A GIVEN NAME.
LH or SK could theoretically change the SSR INFT element, but I wouldn't bother.