The Brill Dictionary of Ancient Greek

Okay, I'll admit to having deliberately bypassed answering this yesterday because a complete answer would be very long. Plus I don't know Greek so I'm not the best source.

Stephen Miller said:

Unlike other Greek lexicons the Brill has 3 entries under δέω.

Other dictionaries have a completely separate entry under δέομαι.

Under δέομαι Brill simply has .....   δέομαι pres. ind. mid., see δέω.

A lemma is an arbitrary unit chosen by those creating the dictionary. In the case of Brill, they choose to consider the Indo-European roots as a means of identifying homographs - words that look the same but are not related as in go the verb and go the Japanese board game. Your clue to this is the Sanskrit reference as Sanskrit has retained a much tighter relationship to the Proto-Indo-European roots than Greek, Latin or Gothic. The tie to PIE roots can either split or combine entries in other dictionaries using different criteria for determining lemmas.

In your case, 1 corresponds to ditá- i.e. «IE *deh1- ‘bind’», 2 corresponds to doṣa- i.e. «IE *deu(s)- ‘miss, want, need’»

Stephen Miller said:

Under δέομαι Brill simply has .....   δέομαι pres. ind. mid., see δέω.

My dictionary lists δέομαι as an Ionic-Attic variant of δέω - as a variant it does not get its own entry but is rather folded into the lemma of which it is a variant ... like liter/litre sharing an entry.

.I don't own the resource to which you refer - I own Beekes, Robert. Edited by Alexander Lubotsky. Etymological Dictionary of Greek. Leiden Indo-European Etymological Dictionary Series. Leiden; Boston: Brill, 2010..But Brill generally includes something like this in its dictionaries:

Beekes said:

Structure of the entry

After the lemma, grammatical information is given between square brackets, for instance, δύρομαι [v.] ‘to lament, bewail’, or ἔγκατα [n.pl.] ‘intestines’. If it is unknown (for instance, in a gloss), this may be indicated with a query.
The grammatical information is followed by the meaning of the word. For most of the glosses, an English translation has been provided. Although this is a major break with tradition in Classical Studies, I consider it to be convenient for specialists in other Indo-European languages than Greek. Of course, in many cases a gloss can be ambiguous, but I hope to have been sufficiently prudent in the translations.
At the end of the first paragraph, I give the origin of the word (in abbreviated form) between two arrowheads. The abbreviations must be understood as follows:

«IE» There is a good Indo-European (IE) etymology. The IE root is reconstructed, and in most cases also the formation represented by the Greek etymon. If there are no cognates, but the Greek word looks Indo-European, a reconstruction has sometimes been proposed, too.
«IE?» An Indo-European etymology exists for the entry concerned, but it is not entirely convincing.
«GR» The word was coined in the more recent (pre)history of Greek, and consists of one or more (possibly) inherited elements; however, the formation as a whole was certainly not inherited from IE.
«PG» The word certainly belongs to the Pre-Greek substrate language. The reason for this decision may be indicated with (V), which means that there are formal variants, or with (S) if the word contains a suffix characteristic for Pre-Greek.
«PG?» The word may be Pre-Greek (see above on (V) and (S)).
«LW» A loanword. The donor language is indicated in abbreviated form, e.g.
«LW Sem.» = a loanword from Semitic.
«EUR» A loanword from (one of) the European substrate language(s). Such words are not reconstructible for PIE, but share similarities with words from other European language families (Germanic, Italo-Celtic, Balto-Slavic) that must be due to substrate influence.
«ONOM» An onomatopoeic word.
«?» No good etymology exists, or the etymology is unknown.

The philological information is subdivided into sections in order to make the presentation more transparent:

•VAR Inflectional forms and phonological variants.
•DIAL Dialectal forms. Mycenaean is mostly given in the (approximate) phonological transcription.
•COMP Compounds (only the most common or etymologically relevant compounds are given).
•DER Derivatives.
•ETYM Etymological discussion.

The Proto-Indo-European reconstructions

The reconstructions in this book follow some conventions which deviate from common usage. Let me mention the most important ones:

a) PIE had no phoneme *a. Whenever *a appears in a reconstruction, the stage of language should always be understood as post-PIE.

b) In IE reconstructions, vocalization of resonants and laryngeals is as a rule not indicated, since the consonantal and vocalic allophones were not phonologized in the proto-language. Thus, for the PIE pre-form of βαίνω, I write *gwm-ie/o-. Whenever vocalization is indicated, i.e. *gwm̥-i̯e/o-, this is understood to be a post-PIE development.

c) I follow Kortlandt’s theory of Balto-Slavic accentuation, and adopted his reconstruction of (pre-)glottalized consonants for PIE (see, for instance, on ἑκατόν and πεντήκοντα).

d) It should be noted that the term ‘prothetic vowel’ is used in this dictionary to indicate the vowel (mostly a-) that may or may not be present in Pre-Greek substrate words. In inherited words, a facultative prothetic vowel is not reconstructed any more since it contradicts the laryngeal theory.

Robert Beekes, ed. Alexander Lubotsky, Etymological Dictionary of Greek, Leiden Indo-European Etymological Dictionary Series (Leiden; Boston: Brill, 2010), ix–x.

There should be an equivalent in your resource.

However, from what I see, I would expect that after the active/middle/passive the entries would depend upon what forms are attested to in Ancient Greek . And there appears to be a short form/long form entry distinction at the active/middle/passive level.