Are you saying it is a DOJ lawyer is acting as the prosecutor, the one trying to get the judge to deny asylum?

Yep. Or at least, I was - like you, I assumed it would be DOJ. Turns out that DHS has its own legal department, the Office of the Principal Legal Advisors (OPLA), with more than a thousand lawyers. I never knew. So the OPLA lawyers, not DOJ, are the ones that represent DHS in immigration court:

ice.gov - About ice

As for whether every case has an OPLA lawyer - apparently not. I would have thought that the DHS would have counsel in each and every proceeding, asylum or not, but apparently they exercise discretion in whether to choose to send a lawyer to any given hearing. Not just asylum, but any hearing on any matter. For asylum, the government definitely can take an adverse position on asylum cases, and will even appeal the decision sometimes. I imagine that any of those cases would definitely be staffed by an OPLA lawyer, as well as any that involved novel or complicated legal issues. But for routine, run-of-the-mill asylum cases, apparently they might choose not to send counsel. I imagine that the government would then just appear directly through a DHS officer, but I couldn't find anything that actually says what happens then.