I want to create a vignette effect, but I can't figure out how to open the dialogue box for Lens Correction.
Make sure your document in not CMYK, as the 'Lens Correction' filter only works with RGB or Grayscale documents.
The filter works only with 8‑ and 16‑bit-per-channel images in RGB or Grayscale mode. (source)
First of all, check in Prefs if all Plugins are displayed:
Note: You'll have to restart PS after changes.
What Photoshop version do you use? PC or Mac? Some 32-bit tools got lost when older Photoshop versions were running on a 64-bit system. IIRC on a Mac you were able to force Photoshop to run in 32-bit mode via the Finder info panel.