Not sure it will double in height but maybe, not easy to judge from street scene. What i would say is that its nowhere near its mature size. I will also cause shading as it is due south from the garden. Another issue will be the honeydew (sticky sap) that comes from the tree. This may make future residents want to remove it. Thes can be mitigated to an extent by regular pruning and not putting parking spaces under the tree so look at your layout and see if you can improve. I would think this is where the LPA are coming from when they say future pressure to fell. Root damage to paths is something else they may look at. You will have to optimise the layout to prevent future conflict if you haven't already.
Another issue is access. How do you access the site. See link.
https://maps.google.co.uk/maps?q=Teston+ME185AU&hl=en&ll=51.256443,0.440279&spn=0.000003,0.004007&sll=52.812723,-0.736084&sspn=1.469186,4.103394&oq=me185au&t=h&hnear=Teston+ME18+5AU,+United+Kingdom&z=19&layer=c&cbll=51.256441,0.440466&panoid=yBwr0lX0yZwRgE1SCwhWHA&cbp=12,292.72,,0,4.17
The levels are possibly a problem on the main access road in if the drive is within the RPA. The no dig drive would be on ground that is already elevated and this would make it difficult to get back down to the road level. The road around the corner looks to have better levels.
I assume that the drive is on the side nearest the tree to keep the house out of the RPA? This is good on one and as you keep the foundations out of the rooting area but you would get honeydew on the parked cars. i.e. future pressure to remove. This can be mitigated, possibly by having a car port roof over the drive on piled foundations. You can put guards on your gutters to prevent them becoming blocked by leaves. You need to identify all the reasons that future residents may wish to remove the tree and mitigate these as best you can. These should already have been looked at in your impact assessment and addressed and your appeal statement should also reflect this. Ask them to clarify why they think there will be future pressure, then look at addressing if you can.
You have to provide a convincing argument to counter what the council are saying at appeal. If you address and counter all their issues you have a better chance at appeal. Thats not to say you will win but you will have a better chance. There are always 2 sides. You have to be objective though, dont say that a 15m lime will not increase in size. The tree officer can easily provide evidence that this is not correct from a book or from other trees in the local area. This will not impress the inspector.
Hope this helps,