There can be an "average" even though there isn't an average person.
To get an order of magnitude estimate, there are roughly 600,000 criminal and civil cases filed in state trial courts other than traffic tickets (which also excludes cases which are filed in municipal courts which are predominantly traffic tickets and parking tickets) in Colorado each year, which has a population of roughly 5,000,000, of whom about 4,000,000 are adults who tend to make up the predominant share of defendants. (I exclude appeals treating those as part of the original case.) This is 0.15 lawsuits per person per year - over a 50 year adult life (even though a small percentage of cases involve juveniles too) this would be about 7.5 cases per lifetime. The total number of cases filed in federal court is proportionately so small relative to state court numbers that it can be ignored in this crude approximation. I also ignore for this purpose, tax audits resolved prior to going to tax court or other court litigation.
Omitting arbitration cases doesn't have much of an impact, because people subject to arbitration clauses rarely "pull the trigger" and utilize this option (there are only about 600 consumer arbitrations actually litigated in the United States each year; see also here) and because about 80% of consumer arbitration cases are filed against business entities when they are filed, rather than against individual consumers (something also true in most securities dealer arbitrations). Business to business arbitration is much more likely to be actually utilized but doesn't figure into these statistics.
But, this is both an overestimate and an underestimate. It is an overestimate, because lots of cases are filed against entities like corporations, LLCs, or governments. In raw numbers, however, these suits are comparatively rare (maybe 10% of all cases) even though they are big ones. It is also an underestimate, because many cases have more than one defendant (the average is probably about 2 defendants per case).
So, you are at an average (i.e. "mean") of about 13.5 cases in which a natural person is a defendant per natural person per lifetime.
But, these cases aren't at all evenly distributed.
The vast majority of civil cases filed involve collection of unpaid consumer debts, residential evictions, residential foreclosures, and cases to collect unpaid taxes. (The number of small claims court simplified procedure cases filed is on the order of 1% or less of all cases filed in the court system.)
And a very large share of criminal cases involve crimes committed by a group of people who heavily overlap with those facing debt collection, eviction, foreclosure and unpaid tax lawsuits - poor people and people down on their luck who resort to economically motivated crimes like theft, robbery, and burglary, or crimes related to being homeless like trespassing or loitering. This population also makes up a large share of defendants in lawsuits to terminate their parental rights for child abuse or neglect.
If you are a poor or working class, especially if you are male and under 40 years old, you are likely to be a defendant in far more than the crude average of 13.5 cases in which you are a defendant per lifetime. Something closer to two or three dozen cases in which you are defendant per lifetime is probably closer to the mark. If anything, this is an underestimate.
The civil lawsuits often coincide with periods of involuntary unemployment, come many at a time, and often conclude with a bankruptcy that you file as a petitioner rather than as a defendant.
The criminal cases tend to coincide with being young, more often than not male, and having had a history of getting into trouble since childhood (often due to a substance abuse problem or mental illness). About a third of all convicted felons are alcoholic or drug addicted high school dropouts without a GED, many of whom are also mentally ill. About two-thirds of convicted felons are high school dropouts (about half of whom got a GED in prison). Less than 2% of convicted felons have a college degree of any kind. Misdemeanor criminal cases tend not to be not so demographically concentrated, although the same general trends are present albeit less intensely.
A "law-abiding" poor or working class person can avoid the criminal cases, but often can avoid only a small share of the civil cases that flow from inability to pay mostly due to disrupted income, and not from bad motives or unreasonable personal finance decisions.
For "middle class" people, the most common reasons to be a defendant are as a defendant in a lawsuit for damages from a traffic accident in which you are (allegedly) at fault, in slip and fall accidents related to your home, in boundary disputes with your neighbors related to your home, or in a divorce or custody case. If there are criminal charges against you, they are mostly likely related to misdemeanor conduct while under the influence of alcohol and/or domestic violence allegations. A typical "middle class" person is unlikely to be a defendant more than one to three times in a lifetime.
If you are self-employed or own investment property, you or entities you own are likewise likely to be defendants at some point in relation to those business activities, either out of disputes related to business contracts, or ownership disputes, or suits related to personal injuries or employment cases allegedly related to your business activity. However, many of these suits will be against business companies you own, rather than you personally, but some suits against you personally are still unavoidable. A typical self-employed person or person with significant investment property would likely be sued at least two or three times in a lifetime (more if the business is a big one) in addition to the one to three times typical of a middle class person for a total of three to six times, and you are likely to sue others far more often to collect unpaid amounts owed to you or to evict someone.
If you are not white, or an assimilated Asian American who is fluent in English, all of the estimated lifetime number of cases are likely to be 1.5x to 2x larger per lifetime. Criminal cases are filed disproportionately against non-whites with similar conduct, and civil creditors in practice tend to be less lenient towards you if you are non-white and will tend to sue instead.
Middle class people and people of greater affluence are also likely to be parties to one or more probate proceedings of relatives over the course of their lifetimes, which aren't strictly speaking proceedings in which you are a defendant in most circumstances.
I also exclude adoption, guardianship and conservatorship cases where you are a defendant merely because you are a minor in need of care, or you are an adult with dementia (or some other debilitating condition) and in need of care. Perhaps one in five people will be the subject of such a protective case at some point in their life.
Pretty much everyone gets traffic tickets and parking tickets from time to time. Something like 5 to 10 traffic tickets per lifetime, and 10 to 50 parking tickets per lifetime, would be on the right order of magnitude of the normal range (parking tickets have a lot to do with whether you live in an urban, small town, or rural area).