Bucc being fully flighted I would never take him outside without his harness on, If I did he would be gone. I would never forgive myself if this ever happened.
He didn't like the harness at first but once I got it on him and we ventured outside then he did fine, the first few times he just sat with me and wouldn't fly or do anything, now that he's used to the outside he loves it and will spend hours out there flying around and having a real fun time.
Is Lilly fully flighted or clipped? Is she harness trained? If not I would try to work with her on getting her harness trained, it is a really safe and fun way to have your birds outside.
With Bucc I had to wear it on me for a while so he could get used to it, (Greys are famous for not liking new things) then placed it on the top of his cage then held it up to him, then laid it on his back. It was a long process.
You may be lucky with Lilly in that she will accept new things, you would need to let her know that this strange thing is not going to hurt her and it will be fun. Maybe give her some treats along the way, Some birds take to it really quickly others take time. A friend of mine had parakeets and she puts a harness on her birds with no problems at all,