Day Trips from Lausanne?

We're not hikers, but love scenery and exploring cute towns and eating and drinking!

If you take the train to Gruyeres, you will find all of that in abundance.

The vineyards along the rail line to Puidoux are nice, but you say you are not hikers, and April could be a little early, but it is generally warm in the area even in early spring.

I'd be very cautious about planning a trip to the top of a distant mountain. The high-mountain transportation options are usually very costly, and clouds could easily move in while you were on the train from Montreux. The usual procedure is to take a look at webcam footage before buying the pricey ticket, but that works best when you're staying quite close to the mountain you're planning to ascend.

Perhaps you can work out a nice loop trip with a stop in a pretty town like Grueyeres.

Take the train from Lausanne to Martigny and then transfer to the train that goes over the mountains to Chamonix...a beautiful day trip! Zermatt is quite a bit farther and will cost you a million times more than Chamonix! Since you have three full days watch the weather for the clearest day and plan to go then whether you end up choosing Chamonix or Zermatt - if it's cloudy it's a wasted trip. You really can't lose whichever you choose!

While you are in Lausanne, you might enjoy an art museum filled with the art done by mental patients.
I found it fascinating.

https://www.artbrut.ch/en_GB/authors/the-collection-de-l-art-brut