Answer:
Option B, Thursday is Lisa's birthday and we'll take her out to dinner
Step-by-step explanation:
The correct sentence among the given option is
Thursday is Lisa's birthday and we'll take her out to dinner
Option A is incorrect because the two sentences "Thursday is Lisa's birthday" and "we'll take her out to dinner " are complete sentences that individually make sense and in order to join them a conjunction or right punctuation is required.
Option C and D are incorrect because the two sentences can be joined by a comma when one of the sentence is dependent on the other sentence for making a complete sense.