How important is the date of the last menstrual period in relation to the actual ultrasound dating?

Depends: For an early sono the LMP is less significant since early on, the sono dates are felt to be more accurate. If a patient shows up in the third trimester for her first sono the LMP dates are more important since they are usually a better guess of the actual fetal age. The sono is then used to try to estimate fetal size and growth on subsequent scans.