Reply from Middlesbrough Council:
I received an email from our contact centre this morning from yourself with regard to the ASL at Marton/Ladgate lane cross Roads. I have had a look on google maps Street view, and from my own knowledge can confirm that the sign that you refer to is not related to the ASL.
The sign here relates to the left-hand turn lane for vehicles on Stokesley Road. If there are pedestrians using the pelican crossing on Ladgate Lane (crossing from near the petrol station towards Marton Manor), a sensor stops the traffic flowing left until the road is clear for vehicles to use. Hence the 'wait here for left turn arrow' sign.
The off carriage cycle path along Stokesley Road ends with a give way sign into the ASL at the traffic lights. Cyclists must only enter the ASL if it is clear to do so, hence the give way markings. The ASL is in place to allow cyclists to get in front of the waiting traffic at the lights, not when the traffic is flowing. The ASL helps to perform manoeuvres such as the right turn onto Ladgate lane as you suggest. If the traffic is not flowing, cyclists can get into the ASL and position themselves in anticipation of the lights changing and the manoeuvre to be completed when the traffic lights allow so.
I hope that this has helped to clear up any confusion, however if you would like to discuss this further, please feel free to contact myself via email or the address/phone number below.
Regards
Chris