thank you for sharing your question with the Wefugee Community!
Unfortunately I have no knowledge of the UK legal system. But I did some research and found this website of the UK government. It basically explains who is eligible for family reunion to a EU or EEA family member in the UK. It states that family reunion might even be possible without being legally married (considering all the circumstances of your case). I thought this information might be interesting for you:
I hope this maybe helps you a little bit further. Maybe there is even someone in the Wefugee Community who has knowledge of the UK legal system and give you more information, esp. about the recognition of a marriage in Lebanon.
All the best