U.K. doesn't accept Wet Green Card Stamp (Form I-551)

You’ll need a visa to pass through the UK in transit

You should apply for a Visitor in Transit visa if you arrive on a flight and will pass through immigration control before you leave the UK.

Transiting without a visa

You might be eligible for ‘transit without visa’ if:

• you arrive and depart by air
• have a confirmed onward flight that leaves on the day you arrive or before midnight on the day after you arrive
• have the right documents for your destination (eg a visa for that country)

One of the following must also apply:

...

• you have a valid USA I-551 Temporary Immigrant visa issued by the USA (a wet-ink stamp version will not be accepted)

https://www.gov.uk/check-uk-visa/y/lebanon/transit/somewhere_else/yes