Our current lexica for Hellenistic Greek fall into two categories on the basis of their approach. The more traditional ones offer suggested translations (not real definitions) and examples of usage. The UBS lexicon classifies words on the basis of perceived semantic domains, grouping words with overlapping meaning into sense categories.
What I envision for a future lexicon is one that does not fit comfortably into either of these categories. It would provide examples of usage, of course, but it would provide a definition along the lines of modern dictionaries such as http://www.merriam-webster.com, and the discussion of examples should be different from what we currently find. Entries for nouns, for example, would also include information on the types of predicates for which the noun may function as an argument.
Let’s look at ἔλεος as an example. As something to be thought of (desired, neglected, remembered), ἔλεος functions as an argument of verbs like θέλω, ἀφίημι, and μιμνῄσκομαι:
1. ἔλεος θέλω καὶ οὐ θυσίαν· (Matthew 9:13 and 12:7)
2. ἀφήκατε τὰ βαρύτερα τοῦ νόμου, τὴν κρίσιν καὶ τὸ ἔλεος καὶ τὴν πίστιν· (Matthew 23:23)
3. μνησθῆναι ἐλέους (Luke 1:54)
When used to speak specifically of something that transpires between two people (where an English translation might speak of showing mercy), though, ἔλεος may serve as an argument of ποιέω. It is not an attitude to be shown or demonstrated, but an action to be done.
4. ποιῆσαι ἔλεος μετὰ τῶν πατέρων ἡμῶν (Luke 1:72)
5. ὁ ποιήσας τὸ ἔλεος μετ᾿ αὐτοῦ. (Luke 10:37)
Notice the usage of a prepositional phrase μετά + genitive to modify ἔλεος in this sense.
In the catholic epistles we find ἔλεος used as an argument of δίδωμι and λαμβάνω in contexts where it involves an interaction between two parties. Ἔλεος is presented as being transferred from a giver to a recipient:
6. δῴη ἔλεος ὁ κύριος τῷ Ὀνησιφόρου οἴκῳ (2 Timothy 1:16)
Two verses later what is given (δίδωμι) is not ἔλεος, but the ability to find (εὐρίσκω) ἔλεος.
7. δῴη αὐτῷ ὁ κύριος εὑρεῖν ἔλεος (2 Timothy 1:18)
Here, ἔλεος functions directly as an argument of εὑρεῖν.
8. ἵνα λάβωμεν ἔλεος (Hebrews 4:16)
Here the focus is on the receiver rather than the giver, but ἔλεος remains a thing to be transferred from an actor to a recipient.
Still, in James 2:13 we find ἔλεος again as an argument of ποιέω:
9. ἡ γὰρ κρίσις ἀνέλεος τῷ μὴ ποιήσαντι ἔλεος·
A lexical entry that takes these examples seriously might define ἔλεος as an action to be done for the benefit of another, despite that other’s lack of merit—an action that can be viewed as a gift in appropriate contexts. But the entry would also need to specify that ἔλεος is never presented as a quality to be demonstrated. In this sense, it is unlike the English word mercy.
This does not mean of course, that we should avoid translating ποιεῖν ἔλεος as show mercy, but it does mean that commentators and even casual readers of the Greek text should recognize that such a translation, while necessary, is required because of the peculiar demands of English, and the image that would come to mind for a speaker of Ancient Greek at hearing ἔλεος was different in important ways from the one that comes to mind for English speakers who hear mercy.