"I am so lucky" would be "J'ai tellement de chance"
"I am lucky" would be "J'ai de la chance".
But you cannot have "tellement" with "du", "de la", or "des". "Tellement" will work with "de" only.
In another example, Duo described heureux as happy or lucky, now it does not accept lucky
how is it determined if it is the masculine or feminine heureuse is used in this sentence?
Heureux is masculine singular and plural,
Heureuse(s) is féminine singular (and plural)
Which begs the question, why is the male speaker using the feminine adjective to describe his own happiness?
There is also an exercise in this section where the female speaker uses the masculine form (heureux) when referring to her own happiness.
Edit: The voice associated with the audio on this comments page is female, but on the "type what you hear" exercise page, it is male.