The second possibility is that the Leukaspides referred to ethnically non-Macedonian troops hired as auxiliaries or mercenaries who fought using thyreos shields, which were wooden, oval-shaped, and covered with hide or felt.
According to Dionysius of Halicarnassus, some Tarentine mercenaries had white shields, and took part at the Battle of Asculum (279 BCE):[1] King Pyrrhus gave the Macedonian phalanx the first place on the right wing and placed next to it the Italiot mercenaries from Tarentum; then the troops from Ambracia and after them the phalanx of Tarentines equipped with white shields, followed by the allied force of Bruttians and Lucanians...
The next notable ancient source discussing the manner is Plutarch's Parallel Lives, in his work on Cleomenes III, which mentions use of leukaspides during the Cleomenean War (229–222 BCE):[1] After Antigonus had taken Tegea by siege, and had surprised Orchomenus and Mantineia, Cleomenes, now reduced to the narrow confines of Laconia, set free those of the Helots who could pay down five Attic minas (thereby raising a sum of five hundred talents), armed two thousand of them in Macedonian fashion as an offset to the White Shields of Antigonus, and planned an undertaking which was great and entirely unexpected.
Diodorus Siculus mentions white shields being part of the looted spoils of war at a triumph awarded in honor of Aemilius Paullus: Subsequently Aemilius, after arranging splendid games and revelries for the assembled multitude, sent off to Rome whatever treasure had been discovered, and when he himself arrived, along with his fellow generals, he was ordered by the senate to enter the city in triumph.
[1] Plutarch writes that Thracians indeed used white shields at Pydna: First the Thracians advanced, whose appearance, Nasica says, was most terrible, — men of lofty stature, clad in tunics which showed black beneath the white and gleaming armour of their shields and greaves, and tossing high on their right shoulders battle-axes with heavy iron heads.