I think the soil you have might be just fine. Horticultural lime is generally pulverized limestone and I've read that sometimes it contains dolomite, which is a limestone-like mineral composed of magnesium carbonate and calcium carbonate. Either one is alright, especially in that soil, where it has doubtlessly been added because it brings the soil's pH up - otherwise it might be too acid since it's made largely of humus (often acidic) and peat (always acidic) and would only be present in enough quantity for that purpose. I'd guess that the soil and the lime would both affect the pH of the water to similar degrees and remain in balance, unless the acid is more soluble in which case the balance of the pH will be lower. I'm pretty sure that calcium carbonate (limestone), which dissolves pretty slowly, would not outstrip the soil when they're underwater any more than it would terrestrially.
Limestone provides calcium (an important trace mineral) and carbonate, both of which contribute to "hardness." It also may contain other trace minerals. And, in the case of your submerged soil, aids nitrifying bacteria by preventing the environment from becoming too acid for them.
This is all assuming that the labeling on the soil is accurate and "Horticultural lime" really indicates pulverized limestone rather than slaked lime (calcium hydroxide), which is also used at times to affect soil pH as well as suspended in water for a bioavailable calcium supplement for saltwater aquaria called "kalkwasser." It is rather caustic (used in lye-free hair relaxers and Nair brand depilating cream) and could be a bad thing in the tank except it would be present in balance with the acidic soil components to arrive at a reasonable pH, as your soil certainly has. At any rate, it is rather unlikely to be slaked lime though it is possible. Another compound called lime is also called quicklime - calcium oxide. I just mention it because somebody may tell you that lime is a calcium oxide based product, which horticultural lime definitely isn't. Anyway I, personally, wouldn't worry about the lime. Anyhow, I noticed you keep guppies. THEY will love the lime in the water - just like home!
My main problem with the soil is the perlite. It will magically work its way up and out of the substrate and float around being annoying. I promise you this. However, there is a simple solution; dump your soil into a big tub of water and swirl it around a bunch and the perlite and other buoyant annoyances will float. Skim or poor them off and allow the soil to settle. If you like, leave the soil in the water for days and weeks, measuring for ammonia. Eventually the most readily decomposed organics will finish decomposing and releasing ammonia. Also, the soil will cycle and when you set up your tank with it, it'll be pre-cycled. You can just keep your soil in water and let it decompose to its heart's content - the organic content will continue to diminish while the minerals remain dip into it whenever you want to set something up with soil substrate. Also, the tannins will all leach out finally and if you change the water every so often, you'll have nice mineralized, cycled soil which leaves your water clear and isn't very prone to mucking up the view when it's disturbed in the aquarium.
Another thing to look for in potting soil is "mushroom compost," which is very nutrient rich but also frequently high is salts. It can be a little too rich and salty for your aquarium depending on how much soil you put in it. Soaking the soil and doing a few water changes will take care of that.
Were I to set up a soil substrate type tank, I'd likely choose a nice, bagged topsoil rather than potting soil but I'd still definitely give it the tub-o-water treatment. I actually have some wood and peat compost based potting soil (contains "horticultural sand," which I suspect is actually lime, mushroom compost, and ground up tree bark) that I used to amend some sand to jumpstart it with some organics to decay and release CO2 and mineral nutrients like mulm does down in a sand bed. It has probably 10% floating crud, it stains the water like a light amber tea, but it has the quality of containing virtually no silt-like or clay-like particles to cloud or haze the water. At any rate, I have it sitting in a big big bucket that I stir up every few days and sometimes change the water in (with conditioned water so the cycle doesn't have to be repeated). It'll be nice to have this soil on hand in a month or so when I am going to be starting a business involving pre-set up low-tech "nature" style nano tanks.
I am considering setting up a test one this coming week using this sand with ~1 mm diameter grains such that it's straddling the gravel-sand boundary as the capping substrate for the soil. I hate gravel, colored gravel, aerators like airstones/air pumps, and flowerhorns (they're just ugly, I mean, come...on!). Just had to interject that, the mention of gravel made it come to mind.
Anyways, I suggest you give that soil the soak-in-a-tub-for-weeks-and-weeks treatment. Or at least give it a few swirls, skim off the floating stuff, let it settle and then repeat several times - removes any excess salts if there's mushroom compost in it and gets rid of haze and cloudiness causing particles.
Don't sweat the lime. I'd use that soil without hesitation if I had it rather than the soil I do have.
