This is the 17702nd most frequent Russian word.
удачливыми
"Удачливыми" means "fortunate" or "lucky" (plural instrumental case).
The use of "удачливыми" here indicates a plural form in the instrumental case, describing a state of being lucky during the trip.
Мы были удачливыми во время этой поездки.
We were lucky during this trip.
Here, "удачливыми" is used after the verb "становятся" to show a transition into the state of being lucky, adhering to the instrumental case requirement.
Они всегда становятся удачливыми после долгого ожидания.
They always become lucky after a long wait.
In this sentence, "удачливыми" connects with the infinitive "быть" (to be), presenting the idea of someone existing in the state of being lucky.