The reason for not mixing old and new batteries is important when the batteries are in series, you cannot get the correct voltage when they are in series.
However, the Lithium Ion batteries are in parallel. You can measure across the battery terminals one at a time after the robot has been fully charged (take the cover off to do this). If the voltage is over 28V, you can use both batteries until one of them fails. If one of the batteries is less than 28V, it might pull down the voltage (not guaranteed). Sometimes a battery will have the right voltage but not put out enough current when it gets old. This type of failure mode works fine in parallel. You just won't get as much current from the second battery, but you will still get some.
If your second battery still works, you will get much longer mowing time, so it sure is worth a try!
