You are eating a deficit, which I believe is due to the reduction in carbohydrates. At least I think so, because the practice is that the deficit comes from reducing carbohydrates. The general opinion is that without the presence of carbohydrates, muscles are more difficult to build.
Low Calorie Diet
With a Low Calorie Diet, all of the Macro Nutrients are low; Protein, Carbohydrates, and Fats.
A Low Calorie Diet limits that amount of Body Weight and Muscle Mass and individual can put on.
The American College Of Sport Medicine, ACSM
Their recommendation for gaining Weight and Muscle Mass is to Increase Calorie Consumption by around 500 calories per day.
The ACSM does not designate where the calories come from.
Ironically, research has demonstrated that the most effective method for increasing Body Weight that Maximizes a Gain In Muscle Mass while limiting and Increase in Body Fat, it to Increase Calorie Intake by approximately 20%.
A 20% Increase in Calorie Intake is approximately the 500 Calories recommended by the ASCM.
With that said, let's break this down.
Carbohydrates
Generally, increasing Body Weight is a little easier when Carbohydrates are increased.
That in part is due due to an increase in Water Weight.
If an individual Carbohydrate Consumption is too high there is a greater increase in Body Fat.
Thus, individuals who decide to Increase Calories by Increasing Carbohydrate Intake need do so slowly.
The amount of Carbohydrates needed are dependent on the Sport or Activity.
Protein Intake
With a Low Calorie Diet, one concern is that Protein Intake may be too low.
Protein Intake of of around approximately 1.6 Time Body Weight in Kilograms or more works.
The Amount of Protein Per Meal
Research by Drs. Donald Layman and Layne Norton determined that approximately 30 gram or higher of Quality Protein (Dairy, Meats, Whey Protein, etc.) per meal elicit an anabolic effect.
Fats
Fat are an easy way to increase Calories.
Fats are necessary for hormonal production. Mono-Unsaturated and Saturated Fat are great sources. Poly-Unsaturated Fats should be limited
Gaining Weight
The first rule in Gaining Weight/Muscle Mass is to Increase Calories, as per the ACSM.
As I have posted multiple times, I have lost with a Low Calorie Ketogenic Diet. I have Gained Weight on the Ketogenic Diet by simply increasing my Fat Calorie Intake.
At one point, I gained 17 on the Ketogenic Diet by dramatically increasing my Fat Calorie Intake.