Difference between "lift" and "lift off" in Feynman Lectures

Solution 1:

The Lexico dictionary shows two meanings for

lift
_VERB

1 Raise to a higher position or level.

2 Pick up and move to a different position.

It is unfortunate that Feynman has created confusion in OP when trying to explain something in everyday language.

As pointed out by @YosefBaskin, the author has used lift off, but it would have been clearer to say remove.

Solution 2:

The verb "to lift" is combined with "off" to form a phrasal verb meaning "to get off the ground" when talking of rockets or aircraft. This is not the verb in question, of course, and the particle (adverb) is not separable; here the basic meaning of "to lift" (Raise to a higher position or level (ref.) disappears because of the adverb "off" that has been added. (Remark: this is mentioned so as to provide an overview of how the particle "off" can be used with a verb or in connection with a verb.)

"Off", as an adverb, can be used with verbs to mean "so as to be removed or separated" (Lexico, 2); the meaning of "lift" is the regular one but "off" adds a precision. In this usage the particle is separable, or rather, so as not to use the vocabulary reserved for phrasal verbs, it doesn't have to be placed directly after the verb and pronouns can be found there instead. This is still not the usage found in the paragraph.

‘If they must graze on the hillside, the reservoir must be fenced off to keep them at a safe distance.’
‘It matters not whether the brandy ignites, but the alcohol must be boiled off.’
‘The second-floor room was sealed off as officers carried out a detailed search.’

(ref. 1) He lifted it off and standing in a holder underneath were twelve wooden boxes.

(ref. 2) When she sidestepped, it made it easier for him to undo the cinch on her saddle. He lifted it off with one hand ...
(same remark as precedingly)

In "we must lift a little weight off the left pan" and in "by lifting a little weight off the other pan", the word "off" is a preposition and has nothing to do with the verb or if it does it is a matter of purely semantic connection (You can lift a dish off a table but you can't think a dish off it); "off" is used to say that something has been removed or separated from something (in these instances, from the pan). (Lexico, preposition 3)

Solution 3:

If I lift Thing X off of Thing Y I remove it from Thing Y.

And, yes, "lift" has two meanings: (1) to raise something higher, and (2) to apply an upward force on something, whether it moves or not.