I would be careful about buying pre-mixed fertilizers without researching them (and how the chemicals interact with each other). Sometimes, they add two ingredients wherein one makes the other less useful. Studying up on chemical salts and how they respond to each other can help you to make a better decision if you're going to get pre-mixed fertilizers. I also recommend learning which chemical salts kill beneficial microbes (e.g. potassium chloride and calcium nitrate) and soil flora.
I don't see any mention of nitrogen levels on the test (just recommendations of how much to add). That would seem kind of unusual, I suppose, but as you're dealing with grass, and you're adding both calcium and potassium, then adding a reasonable portion of nitrogen probably isn't going to hurt, even if you don't need it per se (unless it's very high).
Wood ash contains a fair amount of potassium and calcium. I'm not sure how grass responds to it, but tomatoes sure seem to enjoy some. Wood ash will raise your soil pH.
Greensand is often thought to be high in potassium, and although it does add some, it doesn't add very much; it's probably more helpful for adding silica and changing soil structure.
Bone meal is a natural source of calcium (and other minerals) and phosphorus. I think it may be slow-release. However, if you're getting it to be natural, realize that the stuff they fed the cows whose bones are being used may or may not meet your approval.
Compost can be a good natural source of nitrogen, nutrients and beneficial microbes. Again, if you're composting stuff that isn't organic (e.g. treated with pesticides etc.), some of that may still be in your compost.
I might recommend adding some monoammonium phosphate (you can get granular as well as water soluble). That should add a little nitrogen and a lot of phosphorus. It's not approved for organic gardening, but it seems to be one of the better and safer forms of phosphorus, as far as I've found.
Monopotassium phosphate is great for adding both phosphorus and potassium. It's also not approved for organic gardening and is also one of the better and safer forms of phosphorus, as far as I've found.
Potassium sulfate is good for just potassium. There are forms available that are supposed to be suitable for organic gardening, and there are forms that are not.
I've ordered monoammonium phosphate (both the granular and water soluble forms) and monopotassium phosphate before from Greenway Biotech's website (fast and free shipping; their products seem quite pure and effective). I've ordered AlphaChemicals brand potassium sulfate from Amazon and eBay (mine was purer on Amazon than eBay). I've had good results with all four of these for garden plants (much better than results I've had with pre-mixed fertilizers). I haven't tried these things on lawns, but I thought you might appreciate the information anyway.
I've tried ammonium sulfate and urea from Greenway Biotech's site, too, for nitrogen; the ammonium sulfate has faster and stronger results, in my experience (and is advertized as being good for lawns), but both work better used together on all the plants I've used them both ways with. You might be tempted to use nitrate fertilizers, but be aware there are a lot of issues you might like to know about with those (like toxicity, killing beneficial microbes, stimulating weed germination, and interacting with other fertilizers). However calcium nitrate would add both calcium and nitrogen, and there are likely lots of fertilizer components that interact with others.
AlphaChemicals seems to claim their potassium sulfate is certified for organic gardening (although I haven't been able to verify this). That's the only reason I'd buy their potassium sulfate over Greenway Biotech's, but Greenway Biotech is my favorite place to get fertilizer components and plant nutrients. They have a lot of stuff.
What I've tried from Greenway Biotech all seemed very pure and good (buying directly from their website, rather than Amazon, is nice because they give free two-day shipping by default, and you know for sure it's really the company it claims to be; Amazon's great, and I shop there a lot, but sometimes you have to be careful of companies that seem to be the real company, but actually aren't).
Speaking of purity, you might want to study how various fertilizers or fertilizer components are made (some may be contaminated with such as fluoride or heavy metals due to the process). I researched that sort of thing for a good while before I decided on monopotassium phosphate and monoammonium phosphate for my go-to phosphorus fertilizers.
If you're worried about phosphate fertilizers leaching into the water table, then get the granular kind, which isn't meant to dissolve in water, per se. You may want to get more of it, though (in my experience, it's easier to use up the granular kind faster). If you have a clay-type soil, I imagine phosphorus leaching to the water table might not be as big of an issue as with a soil that drains super fast. I imagine clay filters more phosphorus out, but I could be wrong.
Rock phosphate is another non-water-soluble source of phosphorus. Plants seem to like it, but you'd get a lot more phosphorus from one of the phosphate fertilizers I mentioned above (and there are probably fewer heavy metals in them, too). It's slow-release.
Worm castings can add microbes to help bring out the natural phosphorus in your soil.
Dolomite lime should add both calcium and magnesium as another answerer said. It will raise your pH (and that's usually what people use lime for).
Epsom salt is magnesium sulfate, which also might interest you for magnesium. I'm not sure it's an ideal form, though (at least in our soil), but lots of people tout it for plants as being awesome.
Basalt rockdust has plenty of calcium (and other minerals, especially silica), although I'm not sure how grass likes it offhand. The kind with humic acid added is probably going to have better results to start with (although I haven't tried it), but I have tried the microfine kind, which is pretty cool, and the regular kind (the latter two at least, will raise your pH, however).
I haven't studied the fertilization and nutrient needs of grass much, but this should help you know some alternative sources for fertilizer components and minerals. I definitely recommend reading more about it, as there's assuredly much more to learn (especially as lawns are so common that there is probably a wealth of ideas and information available).