That's really bizarre - what's a lawyer going to write, "yep, that's a name change document all right, appears to be valid (but I'm not the government, I'm just a lawyer)."
It also makes no sense - in Ontario anyway, all lawyers are commissioners to take oaths - so it's practically nonsense, an affidavit is a statement by someone made in front of a commissioner, and here they're asking you to get an oath from a lawyer, who will, I guess, affix his signature saying "I said this."
Anyway, I'm not claiming you've got it wrong, and you can't argue with them if that's what they want, I guess. But as a requirement it doesn't make much sense.
Here's the general form for an affidavit, but again, I think the requirement's silly, this is just to show the facts:
https://www.ontario.ca/page/find-notary-public-or-commissioner-oaths-taking-affidavits
Here's the instructions that say lawyers take oaths:
https://www.ontario.ca/page/find-notary-public-or-commissioner-oaths-taking-affidavits
Bad part is that its a $60-$80 to get an Affidavit here in Winnipeg. I truly don't understand why CGI cannot accept just the name change certificate from the province as during the name change process here in Manitoba you will need to provide your Fingerprints and also need to notarize a Vital Stats form by a lawyer.