Step 1: Identify the time reference.
The phrase “at eight o'clock next week” refers to a specific time in the future.
Step 2: Choose the correct tense.
An action that will be in progress at a definite time in the future is expressed using the
future continuous tense:
\[
\text{will be + verb-ing}
\]
Step 3: Analyse each option.
lying — incorrect; auxiliary verb is missing.
lied — past tense, incorrect for future time.
will be lying — correct future continuous form.
will be laying — incorrect verb; \emph{laying} requires an object.
Step 4: Select the correct option.
Hence, the correct answer is
\[
\boxed{\text{will be lying}}
\]