In one sense, lifetime budget and spend limit share a common denominator - both limit how much money can be spent on an ad campaign. The difference between these two lies in how is this is achieved.
When lifetime budget, as opposed to daily budget, is set, the campaign will run until all of the money has been spent. It doesn't matter how long it takes - be it a day, a week, a year and so on. There is no limit to how much the campaign can cost each day. When the lifetime budget is spent, then the campaign stops delivering.
When daily budget is set, on the other hand, then the ad will run each day until the limit has been reached. When the budget for the day has been exhausted, the ad will be turned off by Facebook until the next day. This will go on day after day and indefinitely unless;
You pause or delete the ad,
You schedule the ad to only run on particular days or,
You set a budget cap. When you set a budget cap, you not only have a daily budget, but in addition, you also have a total budget limit.
Essentially, lifetime budget is like spend limit without the daily budget element. So having a daily budget with spend limit gives you greater control over both your daily and your total spend.