How to update cart.lineItems while specifying HTTP cache headers?
I do not think you can achieve this with browser caching - there's no concept of cache 'escaping' with this type of caching.  Indeed, there's currently no concept of cache escaping with Craft's {% cache %} tag either...which is a shame.

In general, even, caching at the page level when using Commerce carts is tough/impossible - e.g. you'll also need fresh CSRF tokens for cart operations etc.

Currently (without plugins anyway) - the best thing is probably to use Craft cache tags for static page elements and simply avoid caching things like your cart count and add to cart forms etc.  And put your site on a nice fast server :)