How does Customer Lifetime Value $($ CLV$)$ impact the design of customer loyalty programs?

It doesn't; while CLV is a marketing metric, it is used more to determine an advertising budget.

It doesn't; one is financial and one is marketing.

Because CLV can be an important metric and any customer loyalty program will automatically increase CLV

Because CLV provides the monetary 'value' of a customer, managers designing a loyalty program can use it as the return on their investment, and better design a program.