We need to start with a clear decision by the Commons as to what the role of the Lords is to be - is it to have a representative function? If so, then it (a) must be substantially elected and (b) will challenge the Commons and (c) will become party political. Personally, this is the route that I favour - we need a much stronger and more active legislature. If the Lords has no representative function, then election has to be justified as the best way of fulfilling the Lords' other functions - and I have yet to be shown how that could work.
In a Lords (Senate would be better) without representative functions, but needing a concentration of expertise and experience, appointment works. Mostly appointment by the elected, though. It keeps the Lords illegitimate, and allows the Commons undoubted primacy. We could then have party strengths in proportion to votes, quality checks on candidates, a proper balance of race, religion, gender and region - and still do a damn good job.