Using lftp with ssh-agent

I have a script that logs into sftp server

eval `ssh-agent -s`
ssh-add /home/<username>/.ssh/id_rsa
sftp <username>@<target>

This works, but I would like to get only files that are newer than certain date. This doesn't seem to be possible with sftp, so I would like to use lftp

If I try to run the same script with lftp

eval `ssh-agent -s`
ssh-add /home/<username>/.ssh/id_rsa
lftp <username>@<target>

I get a prompt for password. Is it possible to use lftp with ssh-agent or is there some other way to avoid supplying the password?