Levelling Lawn after Small Tree Removal

Hello all

I hope you are well.

I recently had a Dwarf Cherry Tree removed from the Middle of my Front Lawn.

The resulting Damage was an area approximately 4' x 2'.

I Filled the Hole with Top Soil, Watered it to help it Settle, Topped it up, Watered it, Levelled it and then Seeded it.

This is how it looks now:



The Grass Seed has Grown really well, luckily I was able to source the exact Match for my Lawn.

Inevitably, the Area has Settled again, maybe 15mm.

I am looking at Levelling the Area with 70/30 Top Dressing.

I have access to a Lawn Lute which will hopefully make the Task easier.

Am I correct in that I just need to Spread the Top Dressing over the Area with the Lawn Lute to work it into the Lawn?

Do I need to Cut the Lawn Short if I am using the Lawn Lute?

Also, since the Dip is only approximately 15mm can I Level it in one Application?

Thanks in advance

Kevin