“How long can a tooth last without a crown?”

Depending on the condition of the tooth, if it’s in great condition without cavities, gum disease, and/or any fillings, then it can last your lifetime. Again, many factors can affect the longevity of the tooth, even your dietary choice, normal wear and tear, and habits such as grinding or clenching. Visit a dentist to get a definitive answer.

A tooth without a crown for protection will eventually get decay and possibly become infected and require a root canal. The sooner the tooth is protected, the better. It is hard to predict how long a tooth will last without a crown.

It depends on the condition of the tooth and how much healthy tooth structure is left. Also, previous treatment and X-ray and clinical dental exam will help determine.

There is not one simple answer to that question. I'll preface by saying that not all teeth absolutely have to have a crown. However, if a crown has been recommended, the time frame in which you need to address can vary, and it depends on why the tooth needs crowned. If you have a posterior tooth which has been treated with a root canal, you want to crown it as soon as possible. Endodontically treated teeth become brittle and can fracture if uncrowned. If you have been informed your tooth has substantial decay and needs a crown, then that needs addressed soon as possible also. If treatment is delayed, the decay will progress and you might need more than just a crown (root canal or extraction scenario). If you have an existing crown with decay underneath it, that needs a new crown as soon as possible. If your tooth has a symptomatic crack, again, you need to address it soon as possible. An asymptomatic crack however could potentially be monitored for a while if you eat carefully on it and avoid any bruxism or clenching habits. A tooth with a broken cusp, but no decay and no symptoms could remain stable for years without treatment. Some dentists will recommend crowning teeth with large restorations. If there is no active decay present, sometimes these crowns can be delayed for a while with little risk. 
Hope this helped! Listen to the advice of your dentist who evaluated your tooth.