So I took my old and new starter for 98 Ls400 to AutoZone. The gal said both starters are good in their computer but she told me that the old starter goes in and out while it is spinning wherever the new starter spins and stays extended. Is the possible? What is wrong here you all think? Is there a clutch that moves starter in and out throughout the cycle?

 

That's one of a typical symptoms of a short circuited winding. I imagine that one of windings is short circuited.

When the brushes supplies the current to windings next to next, there happens a too big current to the short-circuited wining and this causes a big voltage drop. The voltage drop causes the plunger to retract and the current stops but the inertia keeps the rotor to turn and brushes supply the current to the next good winding. So the starter turns but your type of problem happens.

You can confirm this measuring the resistance of all windings using a mili-ohm meter. One winding will show almost 0 mohm. The resistance of good windings are around 50 m ohms or less and this needs to be measured by a meter which is OK to read very small resistances.