DPI (or PPI) really have no bearing on the quality of the image. The digital image really has no DPI, it only has pixels per inch. For instance, a digital image that is 6000 x 4000 pixels is that size regardless of the DPI or PPI. Changing that setting isn't going to change the number of pixels in any way whatsoever. The image will always be 6000 x 4000 pixels.
A Printers (or a Reprographics Company) will normally set out specifications for a Minimum DPI, the standard being 300.
However, what really matters is the correlation between the final output size and the number of pixels, or what Indesign likes to call the Effective PPI. As long as the Effective PPI is above 300 (240 in your case?), this is normally okay.