I really don’t know the requirements for DOJ employees. IIRC, most of the Clinton WH staff went without clearances, tho I had thought some higher level of security clearance would have been required.
It could be a question of the level of clearance needed for the positions Cruz held. Some clearances are relatively low level and it wouldn’t matter if the person was dual-citizen so long as s/he’d committed no crimes, nor done anything to set off the red flags.
I.e., someone I know worked at the Pentagon and had a certain level of clearance (working in admin offices, nothing super secret so far as I knew). This person also worked at an office within DHS, same clearance (again, so far as I know).
THEN she applied for a job with another govt office that required a high level of clearance and, much to her surprise, she was turned down because she had lived overseas - in an allied country - within the past 3 years. (IIRC at that point it had been 2.75 years, so she could have reapplied 3 months or so later and gotten the clearance and job).
The point being that there are several levels of security clearances, some far more demanding than others. At the lower level, which is probably adequate for DOJ lawyers, you just have to have a clean record. But you have to have a clean record just to practice law.
The forms used for background checks would presumably ask citizenship status. Assuming he filled those out accurately (and I do assume that), he had to be aware that he was a dual national. Why keep it? Its not like travel to Canada is restricted or anything.