So what you end up with could be used as labs maybe, or hooch(much more likely) with some tartness. Taking a simple sugar source and putting in open air like that is also exactly how beer/wine/hooch was made before we were culturing yeast. Yeast moves fast, as fast or faster than lacto at most room temps. Even if you end up lacto dominant, the alcohol content would likely be higher than you are looking for, and it will be more of a mixed culture. This also means the PH may not be as low as you would like. It may still work fine in your applications, it may not.
It’s a real roll of the dice. I wouldn’t do that, or recommend it, if LABS is what you are after.
And airlock is around $4, and you could use it indefinitely and will keep things from getting in. You can get them for buckets, carrots, jugs, mason jars, all kinds of containers. And if you are fermenting things they are really useful.
If you really want to do it how you outlined, at a bare minimum I would say use a known culture to inoculate and use foil as a lid. Gas can escape but it’s much harder for all the airborne micros to find their way in. Use a good healthy known labs culture to start though, and make sure all of you stuff gets cleaned and sanitized otherwise you aren’t giving the lactobacilli a chance.
By skipping the part of the process that helps select for the lacto, you think you are simplifying things, but I think you will find it’s just as likely to make it more complicated, because if you are trying to grow them in an environment that is hospitable to all kinds of micros, you need to have very clean tools and containers, and have you cultures and inputs be clean to get good results repeatedly.
I understand why you have the idea of wanting to skip milk, but please understand that that is a key part in the process. There are work arounds, but to proceed as is with out doing anything, honestly I think that a waste of your time. But hey, it’s your time and your life, go for it if you want. I’m just trying to give you the information and tools to get you what your after.
If it was me, I’d either use a strong fresh labs source, sanitize everything (ingredients included) and do it with a lid, or use a lactose source to select for labs