I think I understand how to ask if something is necessary but how can that necessity attributed to a person or object?

I think these are both correct:
Bugün çalışmak lazım - today it is necessary to work
Bugün çalışmak lazım mı? - is work necessary today?

But how would one attribute that to a person?
Bugün çalışmak lazım mısın? - is it necessary for you to work today?

Look:
http://www.turkishclass.com/forumTitle_6_6377
8th answer

Your second sentence is fully wrong.

Yes you are right on the grammar and yes they are the same.
literal translaton: çalışmam lazım : it is needed me to work

çalışmam = me to work / my working
çalışma = to work / working
çalışmak = to work