how do I get rid of little suckers, which are either from neighbours pine tree or lilac tree sprouted up all over my lawn.
Sprouts of pine trees would not be suckers, because they don't sprout from the roots. However, they could be seedlings. Usually mowing off the seedlings will take care of them.
Many types of lilacs will sprout from roots. Again, mowing may be the best option for control. However, you can also apply sprout inhibitor to the shoots to prevent them from sprouting again. Look for sprout inhibitor at garden centers. It is a type of plant growth regulator.