Yes—Darktable can do film-style color grading, but not necessarily with built-in presets for every named film stock like Portra 400 or Lomography.

From the answers provided:

• Darktable has film-style options via the Color Look Up Table module, including presets such as Fuji Astia, Provia, and Velvia.
• It also supports 3D LUTs, which are commonly used for film simulation and color grading.
• There is a built-in Velvia module.
• Third-party Darktable styles/LUT packs are available from sites like dtstyle.net and other community packs.

So if you want Portra- or lomo-like results, the usual approach is to use a compatible LUT or style rather than expect an exact built-in preset.

For batch editing, Darktable can apply styles/settings across multiple images in lighttable, as long as the LUT/style is compatible with Darktable.

One caveat: film simulation is interpretive, not exact. The final look depends a lot on the source image and processing choices, so results may vary from the original film aesthetic.