I doubt the Lancaster one would be much of an issue provided you went to the eastern side of the M6 as a lot of housing is basically right next to the motorway (including, bizarrely, the quite desirable area of Hala Hill). On the other hand digging up Shap would be rather strongly opposed.
I'm sure there was opposition to the Bay Gateway, but it wasn't really through an area of outstanding natural beauty, just a bit of extra-urban farmland and an industrial estate. There's similarly room to the west of Lancaster along the old railway for a western bypass and third bridge if one is considered necessary* - again, this isn't exactly an AONB, though the inhabitants of rural-feeling Aldcliffe won't approve.
* The M6 effectively provides a bypass of Lancaster itself, but within the city there's no practical alternative to get from north to south than via the city centre, and traffic, particularly industrial lorries, doing this is a serious blight on Lancaster's historic city centre; moving that traffic out would be of considerable benefit, though getting rid of Marsh industrial estate (the only access to which is via the centre) and putting houses on it instead would also solve most of it. That industrial estate access issue also effectively rules out a ULEZ or ZEZ in Lancaster city centre, with higher emissions traffic to other destinations able to use the motorway but not access to that particular industrial estate.