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The verb allĭcĕre was derived from the verb lăcĕre by the preposition/prefix ad ‘to’. It meant ‘to draw gently to, entice, lure, induce (sleep), attract, win over, encourage’. Its principal parts were allicio, allicĕre, allexi, allectum. This verb has not been passed on as a verb to English or Spanish. However, one of the forms of this verb has been borrowed by Spanish in recent times, namely the present participle of this verb which had the regular stem allĭciēnt‑ (nom. allĭc‑ĭēn‑s, acc. allĭc‑ĭēnt‑em) and which was an adjective meaning ‘enticing’. This word was borrowed into Spanish directly from Latin as the noun aliciente, which originally was a fancy word though today it is a very common one (DRAE: 1770).
Sp. aliciente has two primary senses: ‘incentive’ and ‘attraction’. The ‘incentive’ sense is synonymous with incentivo and estímulo, among others, and it translates into English as incentive or inducement, as in No ven aliciente en los estudios ‘They have no incentive to study’ (OSD). The ‘attraction’ sense is less common, and it is synonymous with atractivo and encanto, among others, which can be translated into English as enticement, lure and charm, as in Volver a su pueblo no tiene ningún aliciente para ella ‘Going back to her village holds no attraction for her’ (OSD).
Interestingly, this present participle was borrowed into English at one point as well according to the Oxford English Dictionary, though it does not appear in any other of the major dictionaries of English and the OED marks it as rare. This cognate of the Spanish noun aliciente is the adjective cum noun allicient, pronounced [ǝ.ˈlɪ.ʃɪ.ǝnt], which is primarily an adjective meaning ‘attracting’, according to the OED, first attested in 1831. The noun use of this word is even rarer, and it is first attested in 1658 (OED).
French does have a cognate adjective, which is ‘very literary and rare’ (GR). Its form is alliciant [a.li.ˈsjɑ̃] (fem. alliciante [a.li.ˈsjɑ̃t]). This adjective is first attested in 1866 and thus cannot be the source of the Spanish noun aliciente or the English noun/adjective allicient.
The Latin verb ēlĭcĕre was formed with the variant ē‑ of the prefix ex‑ and, according to Festus Grammaticus, the Latin verb lăcĕre that was obsolete in Classical Latin times. Its meaning was ‘to entice, elicit or coax’ or ‘to draw forth, pull out’. The first three principal parts were ēlĭcĭō, ēlĭcĕre, ēlĭcŭī, ēlicitum. (Note that this derived verb does have a perfect form ēlĭcŭī and even a supine form ēlicitum. This Latin verb was borrowed by English as the verb elicit [ɪ.ˈlɪ.sɪt] in the 17th century with the meaning ‘to evoke or draw out (a response or answer [or reaction])’ (COED). As usual, the English verb was borrowed from the passive participle ēlicitus form of the Latin verb. This verb is homophonous with the unrelated adjective illicit.
Originally this English verb seems to have had the added sense of drawing out or obtaining something by trickery, though that is not the case anymore. This verb has no Spanish cognate. English elicit translates into Spanish by several different verbs, depending on the context, such as sonsacar ‘to winkle out, coax, wheedle’, obtener ‘obtain, get’, when referring to eliciting facts or information, as in obtener información ‘to elicit information’ or sonsacar la verdad ‘to elicit the truth’. Eng. elicit translates as provocar ‘to cause, to start (a fire), to spark off, prompt’ (also ‘to provoke’), evocar ‘to evoke, invoke, etc.’, or suscitar ‘to stir up, arouse, raise, etc.’, among others, when referring to reactions from an individual, as in suscitar un comentario ‘to elicit a comment’ or arrancarle una sonrisa a alguien ‘to elicit a smile from someone’ (Sp. arrancar means literally means ‘to pull off, tear out, etc.)
There is a noun derived from the verb elicit, namely elicitation [ɪˌ.lɪ.sɪ.ˈtʰeɪ̯.ʃən] which means ‘the act or result of eliciting’. This noun is used primarily with the ‘obtain information’ sense of the verb elicit and thus translates into Spanish as obtención or adquisición, or with verbs like sonsacar or obtener used as nouns, as in The elicitation of the true story took time ‘Llevó tiempo obtener la verdadera historia’. This noun was derived in English, from the verb elicit and the Latinate suffix ‑ation (cf. Lat. ‑ĭōn‑). Spanish does not have a cognate of this noun either. Eng. elicitation can be translated into Spanish as obtención, adquisición, when translating the process sense of the word, or respuesta, when translating the result sense.
The verb elicit is used in linguistics and other social sciences to refer to the act of obtaining information from human beings. In linguistics, one elicits information about a language from native speakers, who in linguistic parlance are known as informants (Sp. informante). The techniques used to obtain information from human beings in these sciences go by the name of elicitation techniques, which include interviews, brain storming, focus groups, observation, surveys, and questionnaires, among others. There is no simple and straightforward way to translate the noun elicitation in this context. One possible Spanish translation of Eng. elicitation is obtención (de información, etc.). The term elicitation technique could thus be translated as técnica para obtener información or técnica para la obtención de información.
Another noun derived from the verb elicit is elicitor which refers to ‘someone or something that elicits’. This noun is much less common than the verb elicit or even the noun elicitation. There is also no single word to translate this meaning into Spanish and how the term is translated will depend on the contexts and type of elicitation.
 Eng. informant can also be used as a synonym of informer, that is, ‘a person who gives information to the police about secret or criminal activities’ (MWALD). This sense translates into Spanish as delator, confidente, or soplón, among other possibilities.