Convert lower-case to uppercase with the output to a new column using miller

I want to copy column NAME to column NAME-LOWERCASE. NAME-LOWERCASE should only contain lowercase letters. The uppercase should be untouched in all column expect NAME-LOWERCASE input

NAME,test
PTC,N
Agri,Y
E-example,N
ForYou,N
Willy Nes,Y

output

NAME,NAME-LOWERCASE,test
PTC,ptc,N
Agri,agri,Y
E-example,E-example,N
ForYou,foryou,N
Willy Nes,willy nes,Y

I know how to create a new column from another column and reorder

mlr -I --csv \
    put '$FIRSTNAME = sub($FULLNAME," .*","")' then \
    reorder -f FULLNAME,LASTNAME,EMAIL,DOMAIN,COMPANY input.csv

And I know how to convert upper to lowercase

mlr --csv -N case -l

How to combine both commands? Or there is another miller command to reach my goal?