[tropdrop]

I am also a native speaker. The context I hear it is when, for example, someone wins a game or finds loot within one – "Эх, какой счастливый!...." or "Счастливый человек!" Another example: "у него счастливая рука" (he has a lucky hand [at cards]) [1].

Most dictionaries will offer both happy and lucky side by side (with "happy" being the first definition, "lucky" the second). See the links for some textual examples.

In other households it could very well be that you use "везучий" or "удачливый" more often, but mine (grant it, very far from Moscow) never has.

1 - https://dictionary.reverso.net/russian-english/счастливый 2 - https://dictionary.cambridge.org/dictionary/english-russian/...