I've got a few different things I want to say, in response to different parts of the message.
Firstly, LLL does have to push membership in meetings, it's a non profit organisation, run by volunteers, there may be the odd paid person right at the top, I'm not sure, but it's overwhelmingly run by volunteers, but even an organisation run like that has costs. Unless you are very lucky you'll find you have to charge in some way for an independent support group, which could turn out to be more difficult, if you charge per meeting, it could be discouraging, if you charge a voluntary membership, then you might not get many people join and not being part of a larger organisation you can't spread the load of variation between groups.
I think it would be very hard for a group as a whole to decide to join LLL due to the way LLL is organised, a group needs to be facilitated by a leader, if none of you were a leader, even if many of you joined individually, you still wouldn't be a LLL group, wouldn't have access to the support of LLL, wouldn't be able to advertise yourselves as a LLL group etc.
I'd still encourage you to set up some kind of group, just don't consider it as a potential future LLL group.
But I would encourage you personally to investigate LLL leadership, both for your own development and for the benefit of your community. The costs involved are really not huge, you need to be a current member of LLL, which is $40, though a supporting membership may be sufficient, which is $25. I can't remember the exact term they apply to it, but you'd have to apply as someone not linked to a current leader, which just means you have to have more contact with the person allocated to approve you, rather than receiving some training from the leader, I'm not sure of the precise current cost of application, but it was $31 last year. The only other definite cost is purchasing a copy of "The womanly art of breastfeeding", which I think is under $30. You'll then find there are other books and literature that are highly recommended and it's your own choice what you do about that, you may choose to acquire them gradually over the next few years. I'm not sure if the organisation as a whole has any kind of scheme for covering costs if you can't afford it, but many local groups do, so if that was unaffordable, you could try contacting the leader of the nearest group and see what they suggest!
It's great that there are plenty of knowledgeable people in the area and most of the time that will be sufficient. The advantage of LLL is that if you really need it, you can move upwards through the organisation and ultimately tap into some of the most knowledgeable people on breastfeeding in the world. Also, as it's a large organisation, when a relatively rare problem comes up you can make those connections as they maintain lists of leaders with expertise in specific areas.
You'll also find that if you do decide to work on becoming a leader that there are rules about publicising that, based on the concern that if you identify as associated with LLL, then what you say might be taken to be somehow representative of LLL, or that you'd be viewed to be more knowledgeable in someway, so you'd have to be careful if you do set up a group and are viewed as a leader/organiser of that group that you didn't bring it up in that context that you were a leader applicant.
That probably all sounds very legalistic, but given they celebrated their 50th anniversary last year, they must be doing something right!