All good advice above.
I'm not good at structured training plans. The demands of job and family mean that pretty much any plan I write ends up changing, so I can't advise on that. However, if the long term goal is LEL, then there are three prerequisites:
1) Be able to cycle at a reasonable speed indefinitely. The majority of Audax riders aren't particularly fast (although some are), but they can keep going - so there is a premium on endurance. (After 12 hours of an event my heart rate rarely gets out of Zone 2). However, in my experience, my indefinite speed doesn't improve by riding longer but by riding shorter and harder. Cycle club runs are a good way of doing this, although you'll have to find a group that's comfortable with you riding on fixed as your speed profile up hills may be different than those with gears, which makes it more difficult to ride as a group.
2) Be mentally strong. On a long event there will be times when weather / food / company / route will be against you and it is tough to keep going. I try to build this into my training - for example deliberately making sure I have a headwind to ride into for the last hour of a training ride, or adding in one last hill even though my legs really don't want to. If I haven't had a bad weather ride for a while then I'll go out no matter what into the wind and rain. (the chances of having 4 - 5 wind and rain free days in the UK in July/August are quite low).
3) Manage your feeding. I have yet to see a good article in a regular cycling magazine about feeding for endurance events. On LEL you will probably consume about 4000 calories a day - (the human body doesn't absorb much more) - mostly digested whilst hunched over handlebars with a 25kph wind chilling the stomach. That puts a huge strain on the digestive system, which also has to be trained. What I have learnt (and tried to put into practice having run the catering for LEL controls) is that it takes a while to learn what works for you on an event and develop the ride feeding strategy (for me there are strategic moments when a pork pie, a Twix, a prawn sandwich, milkshakes, or salt-and-vinegar crisps are just what I need; there is also the need for me to manage my caffeine addiction so I can stay awake when night riding - these food preferences might be the end of another rider). That can only be done through experience - so gradually build up your longest ride and experiment. Beyond about 8 hours into an event only a few riders can cope with gels, energy bars and energy drinks. So I would progressively (but occasionally - perhaps once every 6 - 8 weeks) increase the length of your longest ride. The traditional audax sequence of 200km, 300km, 400km and 600km, although not necessary to qualify for LEL is a good long term plan and will help you to learn what works for you in feeding.
Having said that, it's not worth overthinking things. Most of what I've learnt from doing long events and riding longer has been through experience and finding out what works and what doesn't. If you ride your bike and enjoy it you are likely to ride more and get better.