I've recently ordered death certificates from the NJ state archives, and there is an archivist there who has responded to my questions about what they have available now. I can give you her name and email address in a private message, if you'd like.
It took 10 weeks to get the first certificate, and about 5 weeks to get the second one.
If you do find the name and date of death for the person you are looking for, the archive can provide death certificates up to 1930. Their website is not entirely clear about the date cutoff.
Their online order form is also somewhat confusing. It doesn't allow you to attach a file, like a copy of the death index showing the person's name and date of death. But there is a text box where you can describe what you have, though with a ~200 word limit.
Naturally, the online form requires you to put in the names of the deceased's mother and father. However, it will accept 'Not Known', because it thinks this is a parent named Not Known. And Not Known is accepted for both the mother's and the father's names.
Hope this helps.
Lock/Lak/Lok and Kalon in Zagare/Joniskis, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine in Trenton, New Jersey and Lida/Minsk gub., Belarus
Leybman/Leapman/Lipman in Dotnuva, Lith.