Learn Croatian: Naravno, rado ću ti ga posuditi. - Of course, I will gladly lend it to you.

These are all enclitics (short words without their own stress). When grouped together, they form a cluster that follows a strict order. First comes the verb clitic ću (will). Then, for the pronouns, the dative case ti (to you) must always come before the accusative case ga (it). That gives us the exact required order: ću ti ga.

Could the second part of the sentence start with the clitics?

No, because clitics are weak words and can never start a sentence or a new clause. They must lean on the first available strong word. The comma creates a pause, so the next clause starts with the strong word rado. The entire clitic cluster ću ti ga then naturally falls into the second position right after it.

Why isn't the word ja (I) anywhere in this sentence?

Croatian frequently drops subject pronouns because the verb or helper word already shows who is doing the action. The future helper word ću exclusively means "I will", so adding ja is unnecessary unless you want to add strong emphasis (as in "I am the one lending it").

Does posuditi mean to lend or to borrow?

posuditi actually means both! You have to rely on context to know which one is meant. In this sentence, because the speaker is giving something to someone else (ti means "to you"), it clearly means "to lend".