Answer: Cleaning up promtly and rinsing with plain water from the garden hose will dilute the residue and can help prevent damage to the lawn.
Urine spots can also sometimes be reduced by diet change -- but you would need to check with your veterinarian about that.
As far as repairing the lawn, you will need to reseed the bare spots. Loosen the soil down about six inches, work in some good quality compost, then seed and water as needed to keep the spot damp until the grass germinates and reestablishes.
There is nothing you can really do about any darker green patches, but they will normalize in color over time.
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