Just another day doing research

For months now, the research I've done for my novel has involved diaries, books about 19th century American culture, religion and women's issues. Today, I've moved on to time travel...

One of the plot elements I've had in mind since the beginning of the planning for this project was an actual conversation between my two main characters: Lizzie, the 21st century widowed writer who has been unable to write since the death or her husband, and Emily, the 19th century woman whose diary Liz discovers in the attic of her late uncle's Iowa farmhouse.
Thus far, Lizzie has found the diary, read the diary, responded to the diary through her own writing, written short stories based on the diary, dreamt about an argument with Emily over her interpretation of one of the diary stories, and held a written "conversation" of sorts with Emily, while reading the diary account of Emily's courtship with her husband.

Just five minutes ago, Emily walked into the kitchen and asked Lizzie for a cup of tea. Really! (!!)

I've been trying for weeks now to figure out how to make their face-to-face conversation possible (and somehow believable), and every idea I came up with was completely undoable--at least by me. I may have a vivid imagination, but I am too deeply wedded to facts. (I'd never even written fiction until nine months ago, convinced I just couldn't do it). So I decided that I'd abdicate, and just let Lizzie write the conversation for herself. After all, she's a fiction writer.  She should be able to pull it off, right?

How did I know she was going to drag me through time travel movies, books and television as a way to explain what was happening?

Now, let me assure you, there is no time traveling actually happening in my book. Lizzie just wanted to set the scene for her story. I'm trying to reserve judgment until she's finished.

Meanwhile, Lizzie's making tea, and I don't want to miss the conversation that's coming up, so you'll have to excuse me. I need to get back.

(If anyone is going to travel through time, I don't want to miss it!)