I can't say for sure, but I'd like to find out too, as I just picked up a new lemon grass plant. I had a huge one last year, but lost it, and I've never tried feeding it to my birds. I'm thinking that since it is a culinary herb, without any drawbacks for humans, that it would be OK for our birds too. It will be interesting if anyone has done this.
I also want to offer a belated welcome to the forum! I've been off quite a bit lately, so I'm falling behind in welcoming newcomers. There's lots of good reading at
www.finchinfo.com, where there are many articles on nutrition and general finch care.