If we have a spiritual side and I THINK WE DO ...
That is an assertion rather than a fact.
... THEN THERE IS NO CASE FOR THAT NOT TO BE REPRESENTED in the House of Lords considering what is represented.
And why exactly is that not being represented by the, no doubt, numerous members of the Lords who are religious. There is no evidence , whatsoever, that religious people are under-represented in the Lords. What we are talking about is special automatic places for a the most senior members of just one religion. All sorts of other aspects of life should be represented in the Lords - however none are provided with automatic places.
If you think that need to be represented equates to automatic places, then we need
Automatic guaranteed places for women
Automatic guaranteed places for every racial group
Automatic guaranteed places for LGBT
Automatic guaranteed places for every religion and non religious belief system
Automatic guaranteed places for vegetarians
Automatic guaranteed places for vegans
Automatic guaranteed places for flat-earthers
Automatic guaranteed places for climate change deniers
Automatic guaranteed places for environmentalists
Automatic guaranteed places for trade unions
Automatic guaranteed places for racists
etc, etc, etc
And (in the same manner as the Bishops) those automatic places should simply be allocated to leading members of completely separate organisations on the basis of their position within that organisation.
Problem is that rather than becoming more representative, the Lords would become less representative, as most of us do not feel we are defined by 'memberism' - i.e. the organisations we choose to become members of. And indeed many of the population (maybe most) aren't members of any of these organisations.