Does a land with Landfall trigger itself?

Question

If I already have Ashaya, Soul of the Wild in play, and I play a creature that has a landfall ability, such as Lotus Cobra, does the creature "see" itself and trigger its own landfall ability, similar to cards that say "When [Cardname] or another creature enters the battlefield..." o?

Answer 1

Yes, a creature will trigger its own landfall when it enters as a land.

In your scenario, your creatures are also lands. Ashaya's ability is a static ability, which is always true. There is no delay, and your creatures enter the battlefield as lands.

604.1. Static abilities do something all the time rather than being activated or triggered. They are written as statements, and they’re simply true.

Permanents see themselves entering the battlefield and will trigger all applicable abilities when they do.

603.6a Enters-the-battlefield abilities trigger when a permanent enters the battlefield. These are written, “When [this object] enters the battlefield, . . . “ or “Whenever a [type] enters the battlefield, . . .” Each time an event puts one or more permanents onto the battlefield, all permanents on the battlefield (including the newcomers) are checked for any enters-the-battlefield triggers that match the event.

Permanents see themselves entering the battlefield and trigger all applicable abilities, so creatures entering as lands will trigger their own Landfall ability.

Answer 2

Yes, a permanent will trigger its own landfall ability if it enters the battlefield as a land.

Landfall is an ability word that on permanents indicates that a triggered ability has the condition

Whenever a land enters the battlefield under your control...

If the permanent is a land as it enters the battlefield, it meets the conditions for the ability, so the ability will trigger.