I have just been reading a recent (2017) article. Here is an extract:
Relying exclusively on Pāli sources, we may say that lokāyata originally had one and only one sense, namely, disputatio, the art and science of disputation (see Bhattacharya 2009, 187-92). Rhys Davids, who had proposed a different meaning first, viz., Nature-lore, and/or popular philosophy, also admitted this meaning in case of the Milindapañha in the PTS Dictionary (s.v. “lokāyata”). It has been shown that this meaning holds true for the two Mahāyānī Buddhist Sanskrit works, Śārdūlakarṇāvadāna-sūtra (Divyāvadāna) and the Sad-dharma-puṇḍarīkasūtra (See Bhattacharya 2009, 193-6 and 2012).
Now to other, non-Pāli sources. The first occurrence of ānvīkṣikī and lokāyata in Sanskrit is met with in the Kauṭilīya Arthaśāstra 1.2.1 and 10. Ānvīkṣikī is one of the subjects of learning, vidyās; and includes sāṃkhya, yoga, and lokāyata (1.2.10). There is no unanimity of opinion concerning the meaning of ānvīkṣikī in this particular context – the science of reasoning, philosophy, or logical philosophy or what (see note 3 above). Although later commentators wrongly identify this lokāyata with the Cārvāka/ Lokāyata system, the earliest commentary in Malayalam glosses it as the Nyāyaśāstra propounded by Brahmagārgya (or Brahman and Gārgya), lokāyataṃ nyāyaśastaṃ brahmagārgyoktam (adapted in KA, Ganapati Shastri 1924, 27). This evidently was a pre-Gautama system of logic. So the connection of lokāyata with arguments is presumable. Lokāyata(-śāstra) is mentioned along with the Vedas, grammar, and the study of the marks of a superman (mahāpurisalakṣaṇa) in several Suttas in the Nikāyas (see the chart above).
Secondly, comparison with Sanskrit texts, however, has led to happy results: for example, the syllabus for studies of Brāhmaṇa boys found in the Upaniṣads (particularly the Bṛhadāraṇyaka and the Chāndogya) has shed welcome light on the meaning of the Pāli word, lokāyataṃ (Jayatilleke  1980, 47). The parallel columns of subjects found in the Chāndogya list, Śaṅkara’s commentary thereon and the Pāli equivalents occurring in the Dīgha Nikāya are illuminating. It is almost certain that lokāyataṃ was nothing but vākovākyaṃ (Chāndogya), explained by Śaṅkara as tarkaśāstraṃ.
A Sanskrit dictionary tells me that ‘tarkaśāstra’ means ’ “science of reasoning”’
It so happens that there is a mention of the lokāyatika brāhmaṇas in the Rāmāyaṇa, Ayodhyākāṇḍa (critical ed. (1960-75) vol. 2, 94.32; vulgate (1983) 100.28), which throws light on the issue. John Muir (see Cārvāka/Lokāyata 1990, 354-8) and T.W. Rhys Davids (see Cārvāka/ Lokāyata 1990, 372) and others had already noticed the passage, but no one paid it the attention it deserves. Chattopadhyaya (1975, 150-1) was convinced that the whole passage was an interpolation. In fact, the passage, although found in all recensions, is almost certainly a later addition. 15 In spite of its dubious authenticity, two verses (crit. ed. 1960-75, 2, 94.3233, vulgate 1983, 100.28-29), even though interpolated after the fourth century, still contain an indication of what the lokāyatika brāhmaṇas meant in the early centuries of the Common Era, long after they were first mentioned in the Pāli Suttas. It may be noted that the word lokāyatika occurs only once, not just in the Ayodhyākāṇḍa, but in the whole of the Rām. The passage indicates another characteristic of the lokāyatika brāhmaṇas: in addition to their fondness for disputation, they did not care for the religious law books, i.e., the Gṛhya-sūtras and the Smṛti texts.
There are more points in the article which I attach here:
Who_Are_the_lokayatika_brahmaas.pdf (267.4 KB)