Unable to share clipboard in iLO remote console

Strictly speaking, I don't think its possible as iLO does not support the clipboard. But you may be able to save some keystrokes...

You can use the iLO virtual media to mount a folder from the client. Put a text file with the commands you want to use in that folder. Open that file from within the remote session (notepad, nano, grep) to get it on the screen of the remote host. Then copy and paste the lines you want with the clipboard of the remote host to a prompt or other window.

There's no ability to copy/paste over an ILO console connection.

If this is a Linux system, is SSH available?
If this is a Windows system, is RDP available?