BTC Lite is an ERC20 token that can have a lot of value in future. No one can deny the fact that tokens that run on Ethereum blockchain can attain a lot of value if marketed properly. There have been many examples in past, the best being the OmiseGo, TenX, Qtum and so on. The BTC Lite which carries BTCL as its symbol is an unusual type of bitcoin. It is a tokenized version of Bitcoin but runs on Ethereum blockchain. BTC Lite has same supply as the Bitcoin so there are total of 21,000,000 BTCL in total. In this way, the tokenized version copies real deal in this regard.
Bitcoin, currently is seen more as store of value, like gold, rather than a way of making payments. It has high transaction fees and sometimes takes more than a day to arrive. That may change in distant future once lightning network becomes part of Bitcoin. However those features can take years to come into existence.
What makes the BTC Lite http://btclite.org/ so appealing is its transaction time of less than 30 seconds which makes it much faster than the Bitcoin. Pair that with the small transaction fees of $0.001 and you have a winner. Since the BTC Lite runs on Ethereum platform, you can use any of the best Ethereum wallets to store you BTC Lite.
For instance, you can use the popular MyEtherWallet to store it. Just make a new Ethereum wallet address at that site and transfer your BTC Lite tokens onto it. There is no need to sync entire blockchain since that is a web wallet. Alternatively, you can use the official Mist wallet.
Right now, the pre-sale price of BTC Lite is $0.02 or 1ETH = 16000 BTCL. They seem to have excellent marketing team which definitely gives BTC Lite an edge over myriad of other Ethereum tokens around.