ἀπόλλῡμι I lose; I destroy, ruin

• ἀπώλεσα is 1st aorist in form, transitive: 'I destroyed, ruined something.'
  It is therefore inflected exactly like the 1st aorist tense of -ω verbs.
   
• ἀπωλόμην is 2nd aorist middle, intransitive: 'I was lost, done for, perished, died.'
  And all its forms are consistent with 2nd aorist middle forms, like ἐγενόμην, ἀφικόμην, εἱλόμην....

How do we know that? How do we know that the stem is ἀπωλ- (regular 2nd aorist middle) and not ἀπωλο- (a-thematic 2nd aorist middle)? Because there is only one verb (in the whole of the Greek language) that has a form ending in ομην where the ο is not a thematic vowel ο inserted between the stem and the personal 1st person singular ending -μην, but actually belongs to the stem.
δίδωμι: ἐδιδό-μην (imperfect middle/passive) and
δίδωμι: ἐδό-μην (aorist middle)
(middle voice used in compounds mainly).