You're the one getting paid to do it, what do you think it needs?
Since the report is from Lebanon or any other company looking to sell you product "optimal ranges" are going to be inflated a little bit as compared with you nearest university extension office. Realistically you may not see a huge response from a P application although they show it as low, its definitely flirting with danger and buffering it would give you some insurance (see attached). How deep did you sample? Do you see any signs of a P deficiency like a purple coloration in the turfgrass? P will be tough to incorporate into the soil so an application following aeration would be most beneficial since it doesn't move easily through the soil. What kind of soil do you have?