Can yeast ferment the monomers of sucrose and lactose?

yes

Could you provide back for that?

It's entirely dependent upon which enzymes a particular variety of yeast is capable of producing. There are a blue gazillion of varieties of yeast, and not all are the same. Most are capable of using only fructose or glucose, and sucrose, which is a disaccharide of fructose and glucose. Kefir, for example, is a fermented milk product that is produced using a combination of bacteria and yeasts that can ferment lactose. Lactose is a disaccharide of galactose and glucose. In this case, either the bacteria or the yeast produce the appropriate enzyme to separate the disaccharide into component monosaccharides, and then the yeast can go to work on the glucose portion. There are so many yeasts and so little known specifically about most of them that it is hard to say for sure that there are or are not yeasts that can work on arabinose and others. At any rate, you are likely working with one of the yeast varieties that are commonly used to make bread, and these lack the enzymes required to convert sugars other than glucose, fructose, and sucrose.