Investing in Bitcoin (or other crytpto) is similar to the way it’s done in any other country, you spend your dollars in a crypto exchange for coins. The only issue is that in Lebanon, not all exchanges accept transfers to and from Lebanon except most notably the London-based exchange, CEX.io.
Just read their instructions on their pages to get started.
If your are privacy conscious or don’t want to deal with any exchanges you can go to localbitcoins.com and buy them from someone face-to-face.
Cryptocoins.cc has a list of cryptocurrencies with the exchanges that they can be traded on, so be sure to look at that website.
Another notable exchange is Kraken.com but they will not deal in cash with Lebanon, so for that exchange, and all other exchanges like it, transfer your coins to them through CEX.io or Localbitcoins.com.
Most coins have their own default wallet app which can be installed in your computer or phone, so storing them on you personally in this way is also an option. Just send your crypto back to an exchange (CEX) and sell them for dollars once you want to withdraw your investment.
Edit: 9/Jan/2018 – CEX.io has stopped accepting Lebanese cards some months ago. Contact us for available options in Lebanon.
Edit: 27/1/2018 – See BDL Governor Riad Salemeh say that the Lebanese are “free to buy these types of currencies.”