Will it affect your luck to keep the picked-up cat for a while and then get lost?

Scientifically speaking, it doesn't matter. In some areas, there is a custom that the owner's luck will get worse after the cat is lost.

Customs or geomantic omen believe that cats come to make a fortune and cats come to make a fortune. After the cat got lost, it was considered to have lost its wealth, so its luck was affected. However, the loss of the cat will affect the owner's mentality, which will interfere with work and daily life and distract people from looking for cats.

Solemnly declare: part of this answer is for reference only, so don't be blindly superstitious.