Feats, generally, aren't supplanted by beast statistics. (Though your ability to make use of them may be supplanted.) Alert and Lucky, specifically, still apply in their entirety.
Your game statistics are replaced by the statistics of the beast. (PHB p.67)
To see what is supplanted or augmented, take a look at beasts' statistics. ("Statistic," as a defined term, appears on MM pp.6-11):
- Size. Your size is replaced by that of the beast.
- Type. Your type is now beast, not humanoid.
- Alignment. Not replaced, per Wild Shape.
- Armor Class. Replaced.
- Hit Points. Replaced. So no "Tough" carryover, per both our site and Sage Advice.
- Speed. Replaced.
- Ability Scores. STR, DEX, CON replaced. INT, WIS, CHA not, per Wild Shape. (We'll get to initiative and Alert in a moment.)
- Saving Throws. You retain your proficiencies and choose the higher ability modifier of yours and the beast form's, per Wild Shape.
- Skills. Ditto saving throws.
- Vulnerabilities, Resistances, and Immunities. You've got 'em.
- Senses. Replaced. (Specifically called out: if your humanoid form has darkvision and the beast form doesn't, you've just lost darkvision.)
- Languages. "Your ability to speak... is limited to the capabilities of your beast form." (Wild Shape) But as your mental stats and "personality" aren't changed, I think it's fair to say you still know your languages.
- Challenge. Moot, but in case you care, you now have a CR.
- Special Traits. You've got 'em.
- Actions. You've got 'em. (Including, as was recently asked, Multiattack.)
- Reactions. Sure.
- Limited Usage. Yup.
- Equipment. Beasts don't come with equipment. But if they did this'd be a weird one....
- Legendary Actions, Lair Actions, Regional Effects. Not assumed, per Wild Shape.
"You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so." (Wild Shape)
You gain a +5 bonus to your initiative. You can't be surprised while you are conscious. Other creatures don't gain advantage on attack rolls against you as a result of being hidden from you. (PHB p.165)
Okay, my beast form is definitely capable of taking advantage of all of those. For initiative I now look at my beast's DEX modifier, add +5 from Alert, and that's my initiative modifier.
You have inexplicable luck that seems to kick in at just the right moment. [The mechanism by which we game-play that luck.] (PHB p.167)
My beast form is lucky. Cool.
Some other examples:
Inspiring Leader (targets need to see, hear, and understand you) will likely be a hard sell. Mounted Combat's another one.1 But Mobile and Savage Attacker should work just the same. For that matter, so does Great Weapon Master: note that MM at pp.10-11 specifies that (most) monsters' melee attacks are weapon attacks, even those with "a natural weapon, such as a claw or tail spike."
Ability score increases borne from feats, however, are replaced by beast statistics, as Miniman's excellent answer to that linked question explains.
1 Contrary to what most people say, the most dangerous animal in the world
is not the lion or the tiger or even the elephant. It's a shark riding
on an elephant's back, just trampling and eating everything they see.
-Deep Thoughts, Jack Handey