Does Lotus need to have the right to use Toyota engines in their automobiles?

I was wondering about Lotus,since I know that they have been using Toyota and Mercedes Benz engines in their vehicles. I just want to know if they need get permission and pay Toyota/Mercedes Benz or not for the use of their engines,do they?
Why does Lotus just design their own engines for every car that they built or is it to save money?

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