Wikipedia has some good links on Cyprus and its history, specifically :
For Cyprus in general: http://en.wikipedia.org/wiki/Cyprus
For Lefkara in particular: http://en.wikipedia.org/wiki/Lefkara
The official site of the Cyprus Tourism organization http://www.visitcyprus.com has a wealth of information about Cyprus, history, places to visit etc.
The embassy of Cyprus in Washington DC has an excellent site where you can find just about everything you might want. For a brief summary of the history follow the 'Cyprus Timeline' link at the top right of the page http://cyprusembassy.net
An online copy of the excellent book 'Cyprus Images of a Lifetime' by Reno Wideson can be found at http://kypros.org/Sxetikos/Library/Contents.htm There you will also find an online publication of the book Byzantine Churches and Monasteries, with chapters on the history of Cyprus, old maps of Cyprus, information on the monasteries of Cyprus with links to their sites, Cyprus cookery and much much more. The site is worth a visit for anyone interested in Cyprus.
For concise, well documented information on places to visit near Lefkara the site
http://www.agrino.org/nicosia/larnaca1.htm is a good starting point
The same holds for the site
Check out the site of the municipality of Lefkara http://www.lefkara.org.cy/ for useful information.
The community of Kato Lefkara has a site with a nice history section http://www.katolefkara.org/english/index.html and a lot of information on the village and the lacemaking and silversmithing crafts.
The site of the community of Kato Drys http://www.katodrys.org/english/index.shtm has a very nice history section and detailed description of the churches around the community and their history
Black and white pictures of Lefkara and Cyprus and the account of a British Officer who served in Cyprus during the EOKA uprising in the fifties can be found on his personal site http://www.bobmonty.clara.net
World66 also has a good article on Lefkara http://www.world66.com/asia/middleeast/cyprus/lefkara
Find useful information about Cyprus Property, Taxes, Social Security, Education and much more at Cyprus Property Centre.