In their investigation of lift a finger, the Original Poster has happened across a ɴᴇɢᴀᴛɪᴠᴇ ᴘᴏʟᴀʀɪᴛʏ ɪᴛᴇᴍ (henceforth ɴᴘɪ). These are items that tend to only occur in negative contexts. An example might be the word ever. Consider:
- *I have ever been to France. (ungrammatical)
- I haven't ever been to France (grammatical)
Here we see that ever is ungrammatical in the positive sentence in (1), but grammatical when occurring in the negative version in (2).
As it turns out, there are many types of context which covertly involve some sort of negation. Take for example closed questions:
- Have you ever been to France?
Example (3) is perfectly grammatical. We might wonder why. Well closed questions like (3) clearly allow for two possibilities, on the positive side that you have been to
France, but also on the negative side that you have not. For this reason they are often referred to as 'yes/no' questions or 'polarity' questions. Arguably, it is this negative possibility that that licenses the NPI ever.
But open questions, too, often allow for negative propositions and negative answers:
- When have I ever let you down?
The question in (4) clearly allows for the possibility that the speaker hasn't let the listener down. And here we see, of course, that ever is completely grammatical.
The if-clauses in conditionals are semantically similar to closed questions. Consider the conditional in (5):
- If you have ever been to France, you will have come across ...
The if-clause in (5), just like the question in (3) expressly allows for two ideas, the positive polarity one that you have been to France and the negative polarity one that you have not. And lo and behold ever is grammatical here too!
Notice that it is the semantics that seems to allow for ever here. Other constructions used with a conditional meaning will also allow ever:
- Ever go to France without me and you'll regret it.
The first conjunct in (6), just like a regular conditional protasis allows for both possibilities that you will go to France without the speaker and that you won't.
Certain single word items may also sneakily host semantically negative ideas or entailments. Some examples might be the words only or but (when used with a similar meaning to only):
- You only ever go to France in January.
Although (7) looks like a positive sentence, part of its asserted meaning is:
- You don't go to France outside of January.
And again we see in (7) that ever occurs happily in this environment.
There are all sorts of other situations which covertly involve negative ideas and entailments, for example comparative constructions, but we have probably covered enough here already.
The Original Posters question
The Original Poster asks how one can use the negative polarity item lift a finger, or a phrase with a similar meaning, in a positive sentence. In this case they have in mind that when someone makes even a minimal effort to help a certain group of people (i.e. they 'lift a finger to help'), that group of people will show solidarity with them for ever.
One way to do this is to use the NPI lift a finger in a positive clause which also allows for or entails a negative polarity proposition of some sort. In other words we can use the NPI in a clause which involves some sort of covert negation. Two clear possibilities are 1) to use it in a conditional protasis, or 2) to use it in a clause under the scope of a word like only or but:
- If you even lift a finger to help them, they will be your allies for life.
- You need but lift a finger to help them to secure a friend for life.
- You only have to lift a finger in support and they'll be by your side for ever more.