you can for sure plant and add lime at the same time, BUT that lime will NOT be doing its job till it has time to alter PH, and for lime to work , each particle of lime must contact a particle of dirt,
once that happens the lime will actually alter that particle of dirts Ph
its why its often best to add lime , MIX it by discing in lightly, and then WAITING a few months for lime to work , or liming in winter time , so it can leak its way into soil before spring time plantings!
your food plot seeds will need "X" PH for them to grow, if the soil test showed "X" ph and not ideal for "X" seed, just a dding lime NOW< and seeding, will most likely result in a VERY poor take
as soil ph will not be where it needs to be for the seeds to strive
they MIGHt start off well, and then peter out, or vise versa
depends on what the soil PH is currently at, and the seeds needs, as each stage of the plants growth!
so honestly the best thing you can do, is lime ASAP< and then try and work it into the soil BEFORE seeding!
LIEM works VERY SLOWLY too, don't exoect magicto happen fast with it
and liming soil is not a once and done deal, its a task of doing as often as needed to maintain the PH you desire/or plantings need!