Press Alt+F9 to display field codes. To each REF field (which are used
for cross-references), add \* lower. For example: Change
{ REF _Ref146948309 } to { REF _Ref146948309 \* lower \h }. When you
are done, make sure to select the whole document and then press F9 to
update fields. Press Alt+F9 again to hide field codes.

You can use find and replace to automate this: First, type \* lower
in a document and then cut it to the clipboard. Make sure that field
codes are displayed, and then, on the Edit menu, click Replace. In the
Find and Replace dialog box, click More to display all options. Check
the "Use wildcards" option. In the "Find what" box, type <REF *>. In
the "Replace with" box, type ^&^c. Then click Replace All.

Note, however, that the find and replace described above will add
\* lower to ANY cross-reference field, not just to figure captions.