Answer: Mature trees do not usually need additional fertilization, especially if you are already feeding the lawn. Your best bet would be to run some basic soil tests and fertilize based on the results. Your county extension should be able to help you with the tests and interpreting the results.
It is worth mentioning however that the trees will be blocking sunlight and rain from reaching the lawn under them and so the trees will be outcompeting the lawn. Most lawn grasses will not grow well under these conditions and so it may be that you would want to consider using a groundcover beneath the trees instead. Your county extension may be able to suggest which types would do best in view of the particular soil conditions and degree of shade under the trees.
In either case it sounds like the trees are truly wonderful specimens.
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