Cemented lawn...

Greetings

I'm a new member who has just noticed that I have a garden after 56 years! Now really enjoying it, and looking forward to my first crop of vegetables, as well as getting the grass into some sort of order. Sadly, when laying a greenhouse base, I managed to slop mortar onto the latter. I scrapped it up straight away, and watered well, although three days later it is decidedly black and not looking happy. I have forked it well, and really drenched , but is there anything else worth adding; maybe some sand?

Incidentally, I bought a new mower this year, my first mulcher. At first I was most displeased; the grass looked a proper mess, more like a field, and the mower seemed to have little effect. Two months down the line it appears a little more presentable, but still bears a close resemblance to a meadow (apart from the black bit). How long should I expect to wait before it looks at all cared for, (and people stop telling me my grass needs cutting)? The muchler is set to the second to lowest height (I was told the lowest is bad for the blade), the grass is about 40 mm long, but only in places - other areas are well below that and have not, apparently, been cut.

 

With reference to your mulcher observation.
I presume a dedicated mulcher, if so no problem running on lowest setting. It will IMO never look as groomed as if cut by a rotary or cylinder collecting clippings.
I run a Viking Mulcher and its specification says 'A mulcher is designed to cut grass so that it is chopped up several times by a special multi-blade and air flow routing in the cutter area to produce very tiny bits of grass. The cuttings are evenly distributed and left lying almost invisibly on the lawn where they will soon rot down and perform a fertilizing function.'
You will get what I would term a good utilty finish.
Pros , no clippings to collect, self fertilising function, good for large areas.
Cons, sacrifice a bit on finish, cannot cut as short as with other mowers, possibly thatch build up over time.