I didn’t see that you got a factual answer. (If the answer you got is indeed decipherable, I apologize) From the Wiki article on the Milky Way galaxy:
The sun is ~4.5 billion years old. 4.5 billion / 240 million ~ 18 laps. (Actually, Sun’s age is best figure 4.567 billion years. 4.567 billion / 240 million ~ 19 laps.)
Of course, over the age of the Milky Way, dust has completely obscured the starting line (not to mention the running lanes) so we have no idea how far into the 20th lap we currently have progressed.