a lot (非正式语体用lots）可以是副词，修饰形容词或副词的比较级，意为much.  例如：

He is much/a lot/lots taller than John. 他比约翰高得多。

that old中的that为程度副词，意为"那么”。the monkeys that old=the monkeys which are that old. old在此指年龄大小，（年龄）那么大的猴子/那个年龄的猴子。

But caloric restriction, it kind of shocks the system, and one result is, well, those monkeys on the calorie-restricted diet had lots more naive T-cells left than you'd expect in monkeys that old.

译文：但限制热量会在一定程度上使系统休克。其结果之一就是：吃限制热量饮食的猴子体内的幼稚T细胞比我们期待在同年龄的猴子体内发现的要多得多。