Being lazy- Godzilla gender: Female?

Nope. Godzilla is referred to as a male in BOTH instances.

The former is even called out for being a REALLY REALLY WEIRD male, but a biological male, nonetheless.

The latter, Godzilla is referred to as a he by EVERYONE, even psychics, as is Godzilla Junior. It's unknown if Junior is Godzilla's true son, or if he merely adopted him, but it's a father-son relationship regardless.

The only instance of a female Godzilla member that I'm aware of is in my own fan-fiction writing where I gave Godzilla a daughter instead of the sons he usually has.

^I have a fan-fiction idea where Godzilla Junior, now King of the Monsters after his father melted down, adopts Twin Godzillas; one male called Godzilla III, and one female who I still haven't figured out a name for. I also have a head-canon that Mothra Leo, the only known Male Mothra (from the Rebirth of Mothra trilogy) is Godzilla's illegitimate son. Some of Godzilla's scale were still on Mothra when she laid the egg and they got mixed in. It would explain why Leo was so powerful and had all those lasers.

Anyways, Godzilla is definitely male. There is no question. Otherwise, he can't be called the King of the Monsters.

Like has already been mentioned, Godzilla has always been portrayed as a male, evidenced by his official title, King of the Monsters. His sons, Minilla and Godzilla Junior, are both adopted. They were younger members of his species that Godzilla adopted and raised in order to preserve his kind. It's never clear in Son of Godzilla itself that Godzilla just adopted Minilla, but supplementary materials and Toho's own website confirm that Minilla was simply adopted. Godzilla Junior, Godzilla's son from the Heisei series, is explicitly stated to be adopted and have no blood relation to Godzilla in the film and in informational books. Junior was an unmutated Godzillasaurus that Godzilla raised, with his radiation gradually transforming Junior into another Godzilla like himself.

Even the 1998 American Godzilla, which most fans are hesitant to even consider to be Godzilla, is explicitly said to be a male creature in the film. After analyzing the creature, the protagonist discovers that the creature is "a very unusual he" with the ability to lay fertilized eggs. People often say Godzilla 1998 has to be female because it supposedly reproduces through the process of parthenogenesis, something only female reptiles are capable of, but this isn't the case. The 1998 film doesn't follow actual science very closely at all, and the process of parthenogenesis as it occurs in reptiles wasn't well understood at the time the film was made and is never mentioned in the film. Godzilla 1998 is a male organism that due to its mutated genes possesses the ability to reproduce asexually through its own bizarre process. In Godzilla: The Series, the sequel to the 1998 film, Godzilla's sole surviving offspring is identified as a male and even mates with a female giant komodo dragon and acts as a surrogate father to her offspring. It also lacks its parent's reproductive ability. When its parent is resurrected in the show as a cyborg, the characters explicitly say that it is the other Godzilla's "daddy," rather than its mother.

There are never any female members of Godzilla's kind seen in the films, but non-film media have featured them. Examples are Bijira and Majira, Godzilla's girlfriend and mother, respectively, from the Game Boy Godzilla game, and Gojirin from the Get Going! Godzilland OVAs.