My employer just decided to make the change for the holiday season in order to allow more parking spaces for customers, by establishing a mandatory offsite parking lot where we will be shuttled to work. The shuttle will run continuously, so the timing will be random. It takes me around 8 minutes to drive to work, and I have not been late yet. However, is it now the case that I should leave an extra 15-20 minutes so that I am sure to catch the shuttle and still be clocked in on time, or should I be considered on time and paid so long as I am in the lot for shuttle pick up by my scheduled start time?
Unless your employer announces an alternate policy, you need to arrive 15-20 minutes early and clock in when you actually arrive at the building. It is certainly reasonable to ask your manager whether the company is going to do anything to make up for the extra commute time that they're imposing. A good employer would do something to make up for the inconvenience, even if not fully compensating you, but they are probably under no obligation to do so.
This is the sort of thing that gets pretty deep into the wage and hour law of whatever jurisdiction you are in and is the sort of question that can and does go all the way up to the Supreme Court. If you really wanted to press the issue, you'd need to talk with an employment law attorney in your state or country not random folks on the internet.
Assuming you are in the United States, California has some of the most employee-friendly labor laws. There was a case that went to the California Court of Appeal that determined that employers do not need to pay employees for time spent riding a shuttle. Note that the case calls the shuttle "optional" but it is optional in the sense that the employee has the option to drive themselves to work, park in their assigned lot, and take the shuttle or to get to work in another way (having someone else drop them off at the entrance being one such option). Now, it is possible that your state/ country has more employee-friendly laws on this point than California does or that a court in your state has made a more employee-friendly interpretation of the law or that a good attorney could distinguish the fact pattern in your case vs this one. Of course, even if an attorney could make an argument, it is probably not a slam dunk case and if the restriction is only for a month or two, the potential recovery for any suit would be minimal so it probably isn't worthwhile to go the legal route.
There is a good answer to a different (and potentially duplicate) question that discusses additional legal opinions on time spent on shuttles.
is it now the case that I should leave an extra 15-20 minutes so that I am sure to catch the shuttle and still be clocked in on time
Yes, that is exactly what you should do.
If for example, your road were under repair and you had to make a detour, you would still be expected to arrive to work on time.
In this case, I would expect you to leave home a few minutes earlier each day during the holiday period. If for some reason you simply cannot leave home any earlier, perhaps you could get someone to drop you off at the front door at work.
If you are still unsure, ask your employer.
Many years ago, I faced virtually this exact same scenario. I worked at a supermarket and usually parked at the far end where the designated employee parking spaces were. The company repaved the parking lot and temporarily moved the employee parking to a nearby lot. Most of us walked, but there was a shuttle car for those who chose not to walk or in case of inclement weather. We were still expected to be on time and were paid only for the time during which we were punched in.
If your employer owns the parking lots which he is now denying access to, and the shuttle optional, then there is no question that your obligation to appear at your workplace (not the parking lot) in time remains unchanged. The shuttle is just one of the means available to you to fulfill this obligation.
If the shuttle transport is mandatory, then you will have to stick to your employers expectations regarding the time when you will be paid - if you value your job and do not want to taint your reputation. You may be able to clarify this with your boss, and may even make an agreement with him/her. Otherwise, if there is no explicit expectation, then your work culture will be a major factor how lenient you can be. In that case it is advisable to err on the side of caution if you value this job.
The legal side of if you should be paid for mandatory commute is another topic, which depends on country and location. Whatever the legal situation, it probably changes little regarding how you will be perceived if you "come late" or "demand payment for the commute".
An argument could be made that that the employer should pay you for the time that he makes dictates over (mandatory commute), since he has no say how you spend your private life. The legal and cultural views are more complex than this and often disagree with the previous statement.