Lime Tree Leaf Problem

We had a look at your leaf and zoomed in as best we could. It could be scale sucking the nutrients from the stems and starving the leaves of moisture and nutrients, We can vaguely see white spots, and the main rib appears pronounced. So it could be a slow starvation causing the browning and brittle appearance.
However, there are most likely several other issues that need to be checked. Here are some websites with great information on lime tree care and diseases. The first website resource covers growing tips and problems and is very informative – http://citrus.myindoorgreenspot.com/icitrus.htm
The second website is from the University of California and has pictures of actual disease processes and insect damage – http://www.ipm.ucdavis.edu/PMG/C107/m107bpleaftwigdis.html