Answer: How deep the grass roots will grow depends upon your soil type and how often the grass is watered. You might want to place 4-5" of barrier between the lawn and flower bed (there are plastic and metal barriers on the market) and then top the barrier with decorative bricks. Standard sized bricks can be laid end to end or even buried half-way into the ground (longways) so you have only 3-4" above ground.
Best wishes with your landscape!
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