Hi Chris:
As per @James Gifford—NitroPress, we can't add a period/full stop to a paragraph style—just formatting
You could add it with a GREP find/change (not a GREP style) but then you'd have to remove it via second GREP find/change each time you updated the List of Figures, which can only pick up full paragraphs, punctuation included. Or again, as per @James Gifford—NitroPress, you could add a GREP style to the LOF entry to just hide the period.

To add the full stop to the captions
Find: (.+)
Change: $1.
Paragraph style: Caption (call it anything)
Assuming all captions are one sentence, to hide it in the LOF:
Create a character style with the color set to none.
Assign the character style as a GREP style to the LOF entry
Apply style: Hide (call it anything)
To text: \.
~Barb