When describing someone's carefree attitude, there are plenty of synonyms to choose from aside from "in a happy-go-lucky sort of way." For example, you could say the person has an easygoing disposition or a lighthearted demeanor. They might be carefree, spontaneous, or inclined to go with the flow. To convey a lack of worry or stress, you could use terms like nonchalant, relaxed, or unfazed. If you want to emphasize someone's positive outlook, consider descriptors like optimistic, cheerful, or buoyant. At the end of the day, the words you choose will depend on the context and the specific nuances you're trying to convey.