I am unclear on what you want. Do you want your heart rate lower or go up the climb faster. Given the same fitness level you cant go up the climb faster AND have a lower heart rate! You have to train your LT to improve it and then youll be able to hold a higher heart rate up the climb enabling you to go faster up it. If you were slower each time you did the climb then I would look at your nutrition strategy. If you are not fueling properly then that could be a problem.
I want to know should I be allowing myself to go above my LT in order to climb faster or should I work more on improving my fitness so I'm not going above my LT and therefore go faster or atleast if I hit my LT I will be going faster
also how long can you be above your LT and recover enough to continue?
I looked at Joe's zones again and I should be able to hold my 5a zone (LT) for 15-60+ mins depending on fitness.... so I guess it is a combination of getting more fit (so im' not approachinmg my LT as fast) and some more LT threshold training (so I can hold it longer and get used to the pain)
since I was doing the climb in less than 15 mins I could have pushed harder even into my 5b zone for a bit although 15 mins is supposedly pretty tough to achieve for 5b
Train LT so you can hold a higher HR longer. Do hill repeats of 5minutes max effort 5-10 min recovery between. This WILL make you a better climber. When every body else is suffering(above or at their AT/LT) you will be able to hold LT(which will go higher as fitness improves) on climbs and you will be able to put in surges(attacks if you will) above LT that will separate the trained from the untrained!!! I did a hill climb of 7 miles in May and my LT is around 165 and my average HR for the hillclimb was 179(ouch).