If an opposing party does not send a discovery request within 66 days of the trial date do we have to send an opposition?

I would serve an objection stating that the requests were untimely.

Discovery closes 30 days before trial. If the request was served less than 30 days then it is barred by the trial date. However some objections are waived if there is no response. So good practice is always object to preserve any objection.

The discovery cutoff in a California state court is 30 days before the first date set for trial. That date can be adjusted only court order. The 30 days could be a day or so closer to trial because the CCP provides that if the date for performing an act falls on a weekend or holiday, the date of performance moves forward to the next court day. The last day written discovery can be served and be timely is 30 days before the discovery cutoff. If the written discovery is overnight delivered, you add two more days (32). If the written discovery is mail served, you add five days (35). If the discovery was served such that the response falls after the discovery cutoff, you are not required to respond. While you are not required to do so, it is good practice to simply serve an objection to the request as requiring an untimely response. Use the formula given above and count out the calendar days. You don't want to be wrong because you have miscalculated the discovery cutoff. I wish you the best of luck.