Question

Let's go and have a drink. We've got___
time before the train leaves (little, a litle the little)​

Answer 1

Answer:

we've got a little time before the train leaves

Answer 2

Answer:

Let's go and have a ‘drink’. We've got a little time before the ‘train leaves’.

Explanation:

Little is a quantifier. It talks about something which is less in quantity. Like for example there is little money left now. Usually we use little in front of ‘uncountable’ or ‘mass nouns’. In this sentence a little is used and not little or the little.  

As time is singular and cannot be measured thus a little is appropriate in front of me. The little specifies an object. Little denotes very less amount.