Learn Finnish: Minä tietäisin, että sinä valehtelet.

This is a key rule of the conditional mood! For verb type 1 (like tietää), the conditional marker -isi- is added to the strong stem. So, while the normal present tense tiedän (I know) uses the weak grade (t changes to d), the conditional tietäisin (I would know) stays strong and keeps the "t".

The dictionary form for "to lie" is valehdella. Why does it change to valehtelet here?

Valehdella is a type 3 verb. Type 3 verbs often work the opposite way to type 1: their dictionary form is in the weak grade (with hd), but their conjugated forms, like the "you" form here, flip to the strong grade (with ht).

Does the word että (that) change the word order of the sentence after it?

No, it doesn't. Just like in English, että simply connects the two clauses. The second clause (sinä valehtelet) keeps its normal subject-verb word order.

Why isn't valehtelet also in the conditional mood to match the first half of the sentence?

Finnish is very literal with its tenses here. You are stating what you would know as a fact in that hypothetical moment. Since the lying is happening as a real action in that scenario, the present tense valehtelet (you are lying) is used after että.