LP is short for luxating patella.  It's very common in yorkies and toy breeds and sometimes does not show up till they are a bit older.  Uni was diagnosed with grade 3 (although according to what I've read I think it's more like grade 2)  It's when the groove that holds in the knee cap (patella) is too shallow and the knee cap pops out of its place, causing mild discomfort to pain in the dogs.  Here's an excerpt from wikipedia:
   
Diagnosis is made through palpation of the knee. 
X-rays are used to further investigate cases. The luxating patella may causes no or very mild symptoms. There may be intermittent limping in the rear leg, and in higher-grade luxations, the lameness can be severe. 
Osteoarthritis typically develops secondarily.
 There are four diagnostic grades of patellar luxation
[4], each more severe than the previous:
 Grade I - the patella can be manually luxated but is reduced (returns to the normal position) when released;
Grade II - the patella can be manually luxated or it can spontaneously luxate with 
flexion of the stifle joint. The patella remains luxated until it is manually reduced or when the animal extends the joint and derotates the 
tibia in the opposite direction of luxation;
Grade III - the patella remains luxated most of the time but can be manually reduced with the stifle joint in extension. Flexion and extension of the stifle results in reluxation of the patella;
Grade IV - the patella is permanently luxated and cannot be manually repositioned. There may be up to 90¼ of rotation of the proximal tibial plateau. The 
femoral trochlear groove is shallow or absent, and there is displacement of the 
quadriceps muscle group in the direction of luxation. 
Have your vet check him out.  Uni hiked up her leg after a too-fun session at the beach.  We have put her on glucosamine supplements since, and she has not hiked up since.