There is no such thing as a universal lens. The shape of the connection, position of the contacts (and electric protocol too), distance between the connector and sensor are all different.
There are adapters to bridge the gap which are mostly used for legacy lenses. The reason is that with those adapters you will lose most communication between the body and lens, so you have to focus manual, probably have to set aperture manually and sometimes will have to use the camera in Manual mode only (no metering).
There two extremely important points to note above:
- If the lens you use (such as ALL kit lenses for DSLRs) does NOT have an aperture ring, you will only be able to shoot at one aperture (usually either the smallest or the largest).
- If you adapt a lens who is supposed to sit closer to sensor, it will be be able to focus very far and you will almost certainly lose infinity focus.
Given all this and my understanding that your lens investment is minimal, I would recommend simply buying the lenses you need for your new camera.