Go for it. While I'm not a huge fan of application of stuff in July, we're almost in August. :-) Ditto there, but if the risk is that you won't get around to doing it when the time is right, it's fine to do it now.

Thanks. Is it important to wait for rain before putting it down?

Nope, you can go whenever. Calcium isn't going to burn, isn't reactive, and won't waft into the air.

I put down 9 lbs/1k of rapid lime in early August. But my ph started at 5.1 so I have a way to go!

Is it too earlt for another 9 pounds now?

Is Sta Green Rapid Rapid lime ok to use? I couldn find another brand near me.

https://m.lowes.com/pd/Sta-Green-30-lb-Lime-Balance-Soil/50189499

Sta Green is a modest speed lime by observation, it's just rapid compared to the big grind extremely slow stuff. I use it myself to maintain the pH as it doesn't release extremely quickly. But at your pH, it'll wear away faster as it's much more soluble in more acidic conditions.

The general rule is to apply every six months. Otherwise, you end up with a high pH band in the upper part of your soil, and the soil change is fast enough that bacteria and fungi have trouble adjusting their populations as the pH alters.

However, that having been said, a pH of 5.1 is absolutely abysmal and not much better than my starting pH in the high fours.

If you accidentally got out your spreader and accidentally dropped another 10 pounds per thousand square feet and accidentally let it water in with rainfall, I wouldn't say a word.

But do expect that your grasses may temporarily become a much paler green color, even somewhat yellow, as the pH rises too fast, bacteria shuffle around in the rhizosphere, and iron release and absorption temporarily goes to crap.

If you'd rather wait until April, that's fine, too.