He likely could.
Tom does take Harry inside his memory of his fifth year, during when he was unleashing the Basilisk on Hogwarts. Before he takes Harry through the memory, he first tells Harry a lie about his being the one responsible for catching the perpetrator rather than being responsible himself.
“I caught the person who’d opened the Chamber and he was expelled. But the Headmaster, Professor Dippet, ashamed that such a thing had happened at Hogwarts, forbade me to tell the truth. A story was given out that the girl had died in a freak accident. They gave me a nice, shiny, engraved trophy for my trouble and warned me to keep my mouth shut. But I knew it could happen again. The monster lived on, and the one who had the power to release it was not imprisoned.” - Harry Potter and the Chamber of Secrets, Chapter 13 (The Very Secret Diary)
Then he takes Harry into his memory, only showing him the parts that would support Tom's version of the story. However, none of it seems clearly false. He shows Harry his going to Headmaster Dippet's office, encounter with Dumbledore in the hallway, and finding Hagrid with Aragog and blaming the attacks on him. None of it is clearly false, but it's only the parts that support his statements.
“I can show you, if you like,’ came Riddle’s reply. ‘You don’t have to take my word for it. I can take you inside my memory of the night when I caught him.’
Harry hesitated, his quill suspended over the diary. What did Riddle mean? How could he be taken inside somebody else’s memory? He glanced nervously at the door to the dormitory, which was growing dark. When he looked back at the diary, he saw fresh words forming.
‘Let me show you.’
Harry paused for a fraction of a second and then wrote two letters.
The pages of the diary began to blow as though caught in a high wind, stopping halfway through the month of June. Mouth hanging open, Harry saw that the little square for June the thirteenth seemed to have turned into a minuscule television screen. His hands trembling slightly, he raised the book to press his eye against the little window, and before he knew what was happening, he was tilting forwards; the window was widening, he felt his body leave his bed and he was pitched headfirst through the opening in the page, into a whirl of colour and shadow.
He felt his feet hit solid ground, and stood, shaking, as the blurred shapes around him came suddenly into focus.
He knew immediately where he was. This circular room with the sleeping portraits was Dumbledore’s office – but it wasn’t Dumbledore who was sitting behind the desk.” - Harry Potter and the Chamber of Secrets, Chapter 13 (The Very Secret Diary)
The locket shows Ron false images of Harry and Hermione, so it's possible for a Horcrux to lie, and proves they aren't limited to "manipulating the truth" and are capable of directly lying.
Considering that Tom in the diary could show Harry his memory in a way that makes himself look innocent, and that the locket could use Ron's feelings and lie to him, it seems likely (though it's not conclusively proven) that Tom could show false memories.