Superman: Doomsday

Lois Lane (Anne Heche) and Superman (Adam Baldwin) are romantically involved, but Lois is unsatisfied with keeping their relationship secretive and confined to the Fortress of Solitude. While digging for a project, workers from LexCorp unearth the spaceship of Doomsday, a genetically-engineered super-soldier. The creature is highly hostile toward anything that moves; it kills the digging crew and begins a bloody rampage towards Metropolis. Superman and Doomsday engage in a battle until Superman kills Doomsday and succumbs to his own injuries.
Lex Luthor (James Marsters) kills his personal assistant Mercy Graves to ensure no one else knows of LexCorp's involvement. The world mourns and Metropolis honors him with a memorial. Superman's friends cope with his death in various ways: Jimmy Olsen takes a job at a tabloid newspaper, the National Voyeur, Perry White becomes an alcoholic, and Lois, who realized that Clark was Superman, visits Martha Kent for counsel.
In Superman's absence, Metropolis is overwhelmed by criminals. Toyman uses a giant mechanical spider to hold children hostage. Lois decides to save them herself, but Toyman tries to kill her and a little girl. Superman digs out of his grave and saves Lois, apprehending Toyman. He doesn't seem quite the same but Lois dismisses it as shock. She becomes suspicious, however, when Martha tells her Clark has not called home.
The resurrected Superman is revealed to be a clone created by Lex from a blood sample retrieved after the Doomsday battle. Lex is keeping the real Superman's body preserved in a tube, unaware that Superman is still barely alive. He periodically tortures the clone Superman in a special lead-lined red-sunlight room with kryptonite gauntlets. A robot from the Fortress of Solitude recovers Superman's body after detecting he was still alive and begins restoring Superman to health. Meanwhile, the clone's attitude darkens when he hears that Toyman killed a child. In retaliation, Superman drops him from a distance so that he falls to his death. The city is stunned and the clone threatens the populace into abiding by the law, convinced that the terror is preventative. This convinces Lois and Martha that that this is not the real Superman.
Lex berates the clone for his behavior, orders him to find Superman's corpse, and threatens to kill him if he goes out of line. The clone deduces that a lead-shielded kryptonite pellet is in his brain, and removes it utilizing his heat vision and a mirror. Lois discovers the truth after tranquilizing Lex and searching his files with Jimmy. They discover that Lex is cloning an army of Supermen. Lex awakens, armed with a gun but the original clone saves Lois and Jimmy. He also destroys the cloning facility, including the yet-to-be-awakened clones. Lex hides in the special room, hoping to kill the clone with the kryptonite gauntlets, but the clone locks him inside and tosses the entire room to the street. This latest presumed murder triggers military action, which fails.
At the Fortress of Solitude, Superman is revived and undergoes intensive rehab exercises under solar energy to bring back his powers. He resolves to help even though his powers are not fully restored. To improve his odds, he dons a black sunlight-absorbing "Solar Suit" and brings a Luthor-built kryptonite gun. The two engage in a massive battle, culminating at Superman's memorial. After the kryptonite gun originally fails, Lois manages to hit the clone with a kryptonite blast; he destroys the gun, leaving only the kryptonite canister. The canister sticks to the clone's chest and Superman vaporizes it with heat vision. Before dying, he tells Superman to protect the people. Lois is sure of the real Superman once he kisses her, and the crowd is similarly happy. At Lois' apartment, Superman reveals himself to be Clark Kent. Lois is caught off guard, but they smile and embrace.
At LexCorp, Lex is revealed to be critically injured but still alive. He smiles to himself musing that there may still be a way for him to destroy Superman.

Question: Lois and Superman are keeping their relationship secretive and confined to where?
Answer: the Fortress of Solitude