The correct option is D because
The clause "she had been practicing since she was a child" depends on the main sentence "Lily's handwriting was very neat", for its full meaning, hence the clause is subordinate, and a subordinating conjunction is used. The subordinate clause is the cause or reason behind which Lily's handwriting was very neat, not supposing which her handwriting was neat, hence the conjunction 'because' is used, as it denotes reason, and option B is correct. The clause is not conditional, it's a reason which took place in the past which is why Lily had neat handwriting, 'if' is a conjunction used for conditional sentences, sentences which are hypothetical; since it's not the appropriate conjunction here, option D is incorrect. 'Though' is used when two sentences or clauses are contrast or opposite in their meaning. As the given clause and sentence both are not contrast in meaning, in fact one is a reason for the other, hence option A is incorrect. 'Besides' is a coordinating conjunction which is used for sentences which are independent in their meaning. As the given clause is not independent, option C is incorrect.