Perseus digital library has quite a few Greek texts and provides access to a few Attic Greek Lexicons.
This entry is from the Liddle-Scott-Jones on Perseus:
θυ_μο-ειδής , ές,
A. high-spirited, τὸ θ. Hp.Aër.12; opp. ἄθυμος, Pl. R.456a; opp. ὀργίλος, ib.411c.
2. passionate, hot-tempered, opp. πραΰς, ib.375c.
b. of horses, mettled, X.Mem.4.1.3; opp. εὐπειθέστατος, Id.Smp.2.10: Comp., opp. βλακωδέστερος, Id.Eq.9.1.
3. Philos., τὸ θ. spirit, passion, opp. τὸ λογιστικόν, τὸ ἐπιθυμητικόν, Pl. R.440e, al., cf. D.L.3.67. Adv. “-δῶς” Hdn.4.3.3.
There should be an acute accent over the "eta" as shown above.
The sentence cited from the Republic is this: "καὶ γυμναστικὴ δ᾽ ἄρα οὔ, οὐδὲ πολεμική, ἡ δὲ ἀπόλεμος καὶ οὐ φιλογυμναστική; οἶμαι ἔγωγε.τί δέ; φιλόσοφός τε καὶ μισόσοφος; καὶ θυμοειδής, ἡ δ᾽ ἄθυμός ἐστι;
καὶ ταῦτα." So here "θυμοειδής" (spirited) is contrasted with "ἄθυμός" (spiritless). I suggest you look into Plato's tripartite soul (especially in the Republic): he divides the soul into the appetitive, the rational, and the spirited. In the Republic, Adeimantus perhaps is an example of someone ruled by the spirited part of his soul (as opposed to say, Glaucon, who seems more concerned with the "relishes", and thus, might be governed more by the appetitive part).