Being able to remove the lifter without removing the manifold may be dependent upon your heads and manifold. I had a bent pushrod incident a while back (a rocker arm adjusting screw backed off). I wanted to check the condition of the lifters without pulling the manifold. I was able to use a magnet in conjunction with one of those pointed scribes (like a dentist uses) to get the lifter all the way up to the gap between the manifold and the head. I was able to examine it that way but it would not physically fit through the opening. I run an Edelbrock RPM manfold and Edelbrock heads. Other head/manifold combinations may have more room to allow the lifter to be pulled up through the gap.
I don't understand how the tool mentioned above to grab the lifter would work. There's no way the lifter will fit through the pushrod hole. If anything, it's got to come out through the gap between the head and the manifold or perhaps through an
oil fill tube or breather baffle if you have one on your manifold.
Chris