Is there a reason that "he lost the book" is wrong? Swahili doesn't differentiate between "the" and "a", does it?
Can someone split the particles of this verb? Is "li" a present tense particle, as "na"? Didn't get that.
Here you go; A + li + poteza
A : third person singular pronoun "he/she". -li-: tense marker (simple past). -poteza: verb root "lose". The infinitive "kupoteza" would mean "to lose" . I hope that helps.
If -poteza: verb root "lose" and -potea: verb root "get lost" then what is the function of the "z"?
It's causative, to lose something is effectively to cause it to get lost.
-poteza (to lose something) is the causative form of -potea (to be lost), which in itself is the applicative form of -pota (to lose, to ruin, or to distort). all of that should be reflected on wiktionary now.
the tree of verbal derivations isn't only one deep as you seem to imply, applicative forms can have their own applicative forms which then have causative or stative forms, etc, etc. plus, i think there can be more than one causative form for a single parent, just slightly different spellings.
I am not surprised you are confused - this is the simple past tense (-li-) turning up in a lesson on the present tense. They seem to have got confused about which questions to put where.
This lesson also includes sentences in the future tense (-ta-) and imperatives (just the verb root and final vowel), not to mention the odd noun (upasuaje = surgery) in the absence of any verb at all.
It looks like they missed that too. Report it (click on the report flag) next time "she" is not accepted.
(In fact, use "she" as often as possible, because the 'default person' is so often a man that we can forget that women exist too.)