Re-lining curtains

[Wingedharpy]

Need some advice from those that know.
My curtain linings in my spare bedroom have just started to perish (small holes where the folds are.
The curtain fabric is in good condition and I don't really want to change them so am considering re-lining the curtains.
Would it be better to take out the old linings and re-new with replacement fabric or could I simply sew replacement fabric over top of old linings?
Thoughts please.

Take out the old linings, copy them and sew new ones into the curtains.
You may be better renewing the heading tape a well

No heading tape needed 7to25 as they just slip on to a curtain pole.
I'm thinking that having the old and new lining together would give extra protection against the sun and help prevent fading. Am I completely wrong thinking this?