This is my first attempt at making limoncello. I used peel from 6 lemons to 700ml vodka, 250g caster sugar, 150ml water. After dissolving the sugar in the water I added the peel and simmered for 15mins, then removed from the heat and added the lemon juice from all 6 lemons. Whilst still slightly warm I added the vodka and poured into a sterilised container and left for about 10 days before straining and pouring into sterilised bottles.
I have made 4 or 5 Limoncello (Lemon and also Lime based) batches and every one of them has been hazy. The last one has (or had until I skimmed it) a layer of oily flotsam - I did taste it - bitter an oily - I am guessing I got waxed lemons by mistake - but it didn't ruin the the actual liquor. The haziness always sets in when I add the lemon juice.
I tend to add the sugar or honey to the spirit and then add the finely pared skins (not taking the pith). Then juice the lemons and freeze. Turn the jar every time you are near it, don't shake. At around 5 days, when the sugar is dissolved and the oils extracted, defrost and add the juice, strain the lot into bottles.
Shop bought Limoncello (at least the ones I have access to) are generally hazy too. I wouldn't worry unless it tastes "off". If it is full-on roiling clouds - it is probably bits from squeezing the lemon. Let it sink and decant.
It is just lemon particles falling out of suspension. These things take time and the particles are too small to easily filter out, so next time just leave the whole thing in your big container until the Limoncello has cleared up a bit, that way your bottles will look nicer.
It may take a very long time to completely get all the particles out of suspension, so you may want to consider how much effort you want to put into this. You should of cause give it a try and wait as long as your comfortable with, but I've had home made wines that looked clear, and even after half a year of waiting to bottle there was still some particles coming out of suspension and giving my bottles a super thin layer of sediment