I started trying to solve this by finding photos from Cyprus. I found some, but they're not very conclusive.
Then I realised we could do this mathematically!
The approximate distance to the horizon from an observer close to the Earth's surface is given by:
where d is in kilometres and h is height above sea level in metres.
Examples:
- For an observer standing on the ground with h = 1.70 metres (5 ft 7 in) (average eye-level height), the horizon is at a distance of 5.0 kilometres (3.1 mi).
- For an observer standing on a hill or tower of 100 metres (330 ft) in height, the horizon is at a distance of 39 kilometres (24 mi).
As you've pointed out, it's about 100km - I plugged it into GMap-Pedometer and reckon it's about 105km.
So solving for h, we find we need to be at a height of 742m above sea level at the closest point.
Unfortunately nowhere even comes close on the eastern side.
So we have one shot - Mount Olympus, which is 1952m.
Solving for d, we can get d = ~170km.
However the distance from the top of Mount Olympus to the nearest point in Lebanon is well over 250km, meaning that NO, you cannot see Lebanon from any point in Cyprus.
EDIT
The highest point in Lebanon is Qurnat As Sawda. So perhaps you can see from Olympus to here? Let's find out:
From the top of Olympus to the top of Qurnat As Sawda is about 302km as the crow flies. If we sum their heights, we get 5040m. To be able to see 302km, we solve for h, and work that out as a mountain which would need to be 6134m high. So again, no, but it is a bit closer :)