virginia
Virginia Driver's Manual, section 2 on page 11 states:
White lane arrows are curved or straight. If you are in a lane marked
with a curved arrow or a curved arrow and the word ONLY, you must turn
in the direction of the arrow. If your lane is marked with both a
curved and straight arrow, you may turn or go straight.
The lane marking doesn't have to include the word only. A curved arrow is sufficient.
The above is from the second paragraph of the section on solid white lines on page 11. The first paragraph includes:
Arrows used with white lines indicate which turn may be made from the
lane.
Earlier in the document, it briefly mentions signs that sign lane turning directions but there's no information on whether signs are required in addition to lane markings.