Answer: If your soil is very acidic, then lime would help grass to grow better. You need to run some basic soil tests and find out what the pH is, then you would add lime if it is indicated by the test results. That is the only way to know whether or not you need to add lime. You should also fertilize on the basis of the test results.
Some easy to grow perennials in your zone would include daffodils and crocus, Baptisia, shasta daisies, peonies, salvia, achillea, daylily (Hemerocallis) and bulb lily (Lilium), black eyed Susan (Rudbeckia), tall garden phlox, the perennial geraniums or cranesbills, and sedums. These all need full sun. For part shade you might try hosta and ferns, Dicentra, Astilbe, and Aquilegia (Columbine). There are many more perennials you should be able to grow.
Your local county extension should be able to help you with the soil testing and interpreting the results. They should also be able to help you analyze the growing conditions where you want to plant perennials and suggest plants that are likely to thrive especially well there.
I hope this helps.
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