When to start: Allow at least 2 working days: that is the longest processing time the authority publishes.
Electronic visa
Fee
Not published
Processing
up to 2 business days
Validity
90 days
Stay per entry
30 days
The Foreign Ministry's consular fee list and the eVisa portal give USD 20 for single entry, USD 35 for double entry and USD 50 for multiple entry. The portal's terms say an application is considered within 2 working days, not counting the day it is filed, and that you must apply at least 3 working days before the planned date of arrival.
When to apply: Apply at least 3 working days before the planned date of arrival.
Lebanon is party to the 1949 Geneva Convention and Uzbekistan to the 1968 Vienna Convention. They share none, so no treaty obliges Uzbekistan to recognize an International Driving Permit issued in Lebanon.
Whether a permit is required alongside your national license is set by national road law, which we have not checked for this pair.
Passport validity — The UK government says that to enter Uzbekistan your passport must have an expiry date at least 3 months after the date you arrive.