How to set the maximum width of a column in CSS Grid Layout?

"The fit-content function accepts one param, the maximum value. A grid column/row with this property set will still take up as little space as necessary, according to its content, but no more than the maximum value."

See this article: Becoming a CSS Grid Ninja!

You can solve your case while still making use of percentage-based maximums:

div {
  outline: 1px dotted gray;
}

.container {
  width: 300px;
  height: 300px;
  display: grid;
  grid-template-columns: 1fr fit-content(20%);
}

.container div {
  overflow: hidden; /* this needs to be set so that width respects fit-content */
}

<div class="container">
  <div>
    some content
  </div>
  <div>
    Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec cursus eu leo ac ultrices. Vivamus ornare, orci sed pretium sollicitudin
  </div>
</div>

<div class="container">
  <div>
    some content
  </div>
  <div></div>
</div>

You've misunderstood minmax function. It first tries to apply maximum value and when that's not possible, it applies minimum.

So to fix your layout, you just need to calculate 20% of your container width, apply it using max-width property for you grid item, and use auto in your grid-template-columns property definition for the second column. Demo:

div {
  outline: 1px dotted gray;
}

.container {
  width: 300px;
  height: 300px;
  display: grid;
  grid-template-columns: 1fr auto;
}

.container > :nth-child(2) {
  max-width: 60px; /* 20% x 300px */
}

<div class="container">
  <div>
    some content
  </div>
  <div>
    Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec cursus eu leo ac ultrices. Vivamus ornare, orci sed pretium sollicitudin
  </div>
</div>

<div class="container">
  <div>
    some content
  </div>
  <div></div>
</div>

Update: More flexible solution will be to use fit-content function from this answer.