How can I solder LCD Pins when solder does not "stick"?
If it doesn't "stick", the best thing to do is use a Flux Pen. These are less than £2 on eBay ( http://m.ebay.co.uk/itm/231227287271 ). These are designed to clean the joint and remove all the oxidastion on the metal parts or legs. 

You almost "draw" with the flux pen over what you want to clean up. It will leave a horrible looking mess, but the solder will then work. The reason solder doesn't stick is because the metal becomes oxodised after a while so the solder won't "stick", as it has no bare metal to stick to!

Also, try using a lower temperature on your soldering iron. It may be too hot to work with. 
If you don't have a temperature controlled one then bin it, and get one as the non-temperature controlled ones are so imprecise and can cause all sorts of chaos like lifted pads and burnt boards! They are generally useless!

Don't forget! Use solder with a flux core. It makes life so much easier!

Some really useful videos on how to solder properly are on the EEVBlog here: 

http://youtu.be/J5Sb21qbpEQ - How to Solder: Part 1

http://youtu.be/fYz5nIHH0iY - How to solder: Part 2 

http://youtu.be/b9FC9fAlfQE - How to solder: Part 3 - Surface mount components. This isn't really as important as the other ones, but it's still really useful to watch!