JH--
to answer your question---lid should be snug not tight
There are few different methods that you can use when fermenting.
1--Leave lid on snug enough for carbon dioxide to escape, the theory here is that as long as carbon dioxide is escaping oxygen cannot enter.
2--Close lid tightly and burp jar every day for about a week
3--Submerge everything beneath the brine so it (fruit) is not exposed to the atmosphere/oxygen.
4--airlock system
You will need to consider a few things when starting up a ferment.
1. Will it be a mash or whole fruit
2. Where will lacto come from, wild or commercial.
If you are going to do a mash then submerging everything will be a little difficult to get all the little bits below the water so you are left with the other three as options.
If you plan to use wild fermentation then it is recomended that you leave the mash "out" or open to the air for 24hrs. Cover with a towel, cheesecloth etc. and scure with rubberband and leave on your counter. Then cover with lid or airlock. I only use wild fermentation when everything is submerged in the brine and I never follow up with a lid, I just leave open to atmoshere. I.E. Pickles or saurkraut place all in stone crockware, I cover with a dinner plate and place 3-4 quart mason jars full of water on top of the plate to keep everything submerged. Times for ferment will depend on temprature, and personal preference anywhere from a week to a month or longer
For mashes I use commercial lacto (whitelabs) from a local homebrew shop to get everything going quickly and assure myself that the benificial bateria are present. I know of others using lacto pills or whey (whey will have a taste on your ferment as an FYI). Then I use burp technique. Once a day I will crack the jar to let the gases escape and then tighten it back up. I will also give the jar a good shake and burp again. By doing this you will know when the fermentation has started and when it finished. No more burps and ferment is complete and starting to age and flavors will start to mingle.
Things to keep in mind--
Leave enough space for ferment, never fill a jar more than 2/3 full or there will be run over.
By tightning lid completly, I think there is a small risk that if left unattended and not burped, jar can crack/explode.
P.S--
you will notice that if you are to buy a commercial airlock system made for fermenting vegetables it also comes with a lid that will fit in the jar and a stainless steel cup, kinda like one served at resturants for condiments. They will intruct you to add lid and invert the cup then attach the lid with the airlock. So everything is submerged. This is a kinda "covering all bases" approach.
Hope this helps, good luck and let us know how it goes
here is a link to a free ebook if interested
http://www.culturesforhealth.com/lacto-fermentation-free-ebook