Those two guys that already answered you are professionals, I'm an amateur, so weigh that up as you read what I've got to say.
First let me say, don't be disheartened by what you see in the Greek. This is one of the adjustments to the basis of faith that we all have to go through when we start to learn Greek. Remember that God's word has always said what it has said, and now, through study of Greek, we are trying to understand it better. There will be many temptation along the way. After you have learnt Greek, remember that others have not, and be gentle with them later, as you should be gentle with yourself and your understanding now. The more you know the more you will have to bear with the ignorance of others - that is the cost of knowledge.
If you want to feel you are right and someone else is wrong, consider the person; they love Jesus, they come to church faithfully, they teach Sunday School and help in the Church working bee - those are really important things, simple things.
Learning Greek restricts
our understanding of the English - that is to say that it makes sure that we understand the correct sense of the English. Greek is a language like any other, and langauges are ambiguous - we can not really be sure what they mean - there are going to be misunderstandings. We are discussing the English word "Lost" here, so let's look at it for a moment.
The English phrase "the lost" could mean a number of things to different people;
- "Lost" could mean that someomne was driving / walking and their memory / map / GPS failed them, and they ended up in a place that they didn't know or couldn't recognise. "The Robinson family and Dr. Smith were lost in space"
- "Lost" could also mean that you had something in your hand / handbag before, but now it is not there. "He's lost the keys to the car again."
- "Lost" could also mean fallen in battle or an accident. "New Zealand lost 7.6% of her men of military age during the great war."
- "Lost " could mean that someone no longer enjoys the use of something. "Many people lost their sight during the era of prohibition from drinking moonshine".
- "The lost" Those who need to hear the Gospel. "Our church is doing its best to seek and save the lost".
People for want of the knowledge of Greek have made a lot out of "Seek and save the lost" and equated "the lost" with those waiting for our preaching in the Great Commission. It starts off in the singular as you have noted, then "the lost" has become plural, because that is the natural way to take it in English. These things were all done with the best of intentions and usually with excellent results. But now, welcome to a scholarly study of the NT in the original language.
τὸ ἀπολωλός is not a group, it is both neuter and singular! After the initial shock!! and horror!! in cases like this we are often left wondering, well if it doesn't mean what I assumed it meant in English, so what does it mean?? Is it Zaccheus or his family or what??
Let's look at Ezekial 34:15, 16 in Greek (called LXX - you can use a search engine to look into that)
ἐγὼ βοσκήσω τὰ πρόβατά μου καὶ ἐγὼ ἀναπαύσω αὐτά καὶ γνώσονται ὅτι ἐγώ εἰμι κύριος τάδε λέγει κύριος κύριος, τὸ ἀπολωλὸς ζητήσω καὶ τὸ πλανώμενον ἐπιστρέψω καὶ τὸ συντετριμμένον καταδήσω καὶ τὸ ἐκλεῖπον ἐνισχύσω καὶ τὸ ἰσχυρὸν φυλάξω καὶ βοσκήσω αὐτὰ μετὰ κρίματος
"I myself will graze my sheep, and I will give them rest, and they will know that I am the Lord. Thus says the lord, the Lord. I will seek the one that is lost, I will return the one who has wanderd away (back to the sheep fold), and I will bind up the crushed, and I will strengthen the abandoned and guard the strong and tend them (all types together in one flock) discerning the individual needs of each"
Jesus is saying that he is here now with Zaccheus in fulfillment of that prophesy of Ezekiel. It is neuter not because Zaccheus or his family are neuter, but because the prophesy is neuter (referring to the sheep in Ezekiel). [The word for sheep is πρόβατον.] Zaccheus is identified as one of the types of sheeps that needs a certain type of pastoral care from the church and her oversight.
The parsing that you have done is a good start, but let's do something else too. Since the English word "lost" has so many meanings it is probably that there is a different Greek word for each of those meanings. To find that easily (and in a not too scholarly way) is to look through an English concordance and find the Strong's numbers for all the times that "lost" occurs in English. That is like a fast-track to understanding synonyms - words which have similar meanings. We could work through that together if you would like to.
Another similar situation that you could consider is, "Study to shew thyself approved." (2 Timothy 2:15). I used to get told that when I was a boy with the meaning, "Go and do your homework" or "Aim to undertake further study", but that is not the meaning of the verse in Greek. You can look for yourself in the dictionary what the meaning of σπουδάζω is, but it is certainly not "doing one's homework".
How about "Don't stand in the way of sinners." (Psalm 1:2) 95% of people reading that in English understand "stand in someone's way" to mean obstruct them (when they are committing a sin), and the other 5% are not interested and want to watch the cricket (or baseball)
. But that is not the meaning in the Psalm where "stand" is one step in the acclimatisation process - you walk, then stand, and eventually sit as you get more used to being a sinner. The opposite of "stand" is "walk on by", "don't stand" = "don't linger about" on the way that sinners take or pretty soon you'll be walking down it too.
Welcome to dealing with the Bible in the original languages.
Οὐκ οἶδα τί λέγεις. ¯\_(ツ)_/¯