A number of old papyri documents seem to reference works that were once popular, but are no longer extant. Does anybody know if anyone in the Classics field has collated a list of all known lost works from that era?
I have a suspicion that you're thinking mainly of the Greco-Roman classical era: it would be nice to be explicit about that.
Economics prevent it from being quite as centralised as I'd like. What we get instead are many collections, divided by genre. I'm going to list off what I believe are the more-or-less standard current editions in each case, but I would love to be corrected and updated where relevant. Since these are standard critical editions, they are mercilessly designed for the specialist. If you want something accessible to a generalist, I can give that in a follow-up, but I warn you now that it's just not going to be thorough.
The biggest ones that come to mind right now are:
Greek historians and geographers: Jacoby (ed.), Fragmente der griechischen Historiker, many vols.; Brill's New Jacoby (an update of the former, with English translations; it's a work in progress).
Greek philosophy: Diels and Kranz (eds.), Fragmente der Vorsokratiker, 3 vols. (1951-1952); F. Wehrli (ed.), Die Schule des Aristoteles: Texte und Kommentare, 12 vols. (Basel, 1967-1969).
Greek poetry: Alberto Bernabé (ed.), Poetarum epicorum graecorum testimonia et fragmenta, 4 vols. (Stuttgart/Leipzig, 1996-2007); M. L. West (ed.), Iambi et elegi graeci, 2 vols., 2nd ed. (Oxford, 1989-1992); D. L. Page (ed.), Poetae melici graeci (Oxford, 1962) and Supplementum lyricis graecis (Oxford, 1974); various eds., Tragicorum graecorum fragmenta, 5 vols. (Göttingen, 1971-2007); Kassell and Austin (eds.), Poetae comici Graeci, 8 vols. (Berlin, 1983-2001); J. U. Powell (ed.), Collectanea Alexandrina (Oxford, 1925); Lloyd-Jones and Parsons (eds.), Supplementum Hellenisticum, 2 vols. (Berlin, 1983-2005).
Latin historians: T. J. Cornell (ed.), Fragments of the Roman Historians, 3 vols. (2013).
Latin grammarians: H. Funaioli (ed.), Grammaticae Romanae fragmenta (Leipzig, 1907) (up to the age of Augustus only).
Latin poetry: J. Blänsdorf (ed.), Fragmenta poetarum Latinorum epicorum et lyricorum (Berlin, 2011).
Works of specific individuals, e.g.
Antimachos: B. Wyss (ed.), Antimachi Colophonii reliquiae (Berlin, 1936) and V. J. Matthews (ed.), Antimachus of Colophon: Text and Commentary (Leiden, 1996).
Didymos: M. Schmidt (ed.), Didymi Chalcenteri grammatici Alexandrini fragmenta quae supersunt omnia (Leipzig, 1854)
Eratosthenes: D. W. Roller (ed.), Eratosthenes' Geography (Princeton, 2010)
Krates of Mallos: M. Broggiato (ed.), Cratete di Mallo: I frammenti (La Spezia, 2001)