Minderwiz
Those two quotes above are from two online astrologers claiming to practise traditional and should make what I meant clearer when I stated modern and even many traditional astrologers state Lots need power from planets (via aspects) to even have an effect.
A question-one traditional astrologer stated spiritual life and religion can be determined using ARabic Parts specifically Part of Spirit. I already know you stated the traditionals did not view spirituality in this way but there is so much stuff I don't know where to begin.
Obviously they've never read any traditional texts! Lots are only calculated if you need to know something in more detail. Most of them (with the exception of the Hermetic Lots, plus Basis and Exaltation) are Topic based. You have a Lot of the Mother in your chart. Most people would consider it important to know something about your mother, they wouldn't dismiss your mother as being irrelevant because the Lot of the Mother ws not aspected.
You have a Lot of Marriage in your chart. Again most people would consider it important, even if it shows your chances of marriage are low. I repeat what I said in the post above. Lots are not active. They are used to identify the planets that signify those topics. The position of the Lot in your chart will have relevance through it's relationships to the Ascendant and the Lot of Fortune.
Lots may or may not be aspected. They don't get power from the aspects, though they do get bonified (made more favourable) or malefied (made less favourable).
Some Lots will be totally irrelevant even if they are hard aspected by every planet. For example the Lot of Barley never have any importance to you - unless you become a trader in Barley.