The total cost of the most efficient lined Trapezoidal channel can be calculated by considering several factors such as the discharge, channel dimensions, material costs, and construction costs.

1. Determine the required discharge:
The first step is to determine the required discharge for the channel, which is typically given in cubic meters per second (m³/s) or liters per second (L/s). This information is crucial as it helps in determining the dimensions of the channel.

2. Calculate the dimensions:
The dimensions of the trapezoidal channel can be calculated using various hydraulic equations and design criteria. The channel's cross-sectional area and hydraulic radius are important parameters in determining the dimensions. The dimensions will depend on the discharge and the desired velocity.

3. Determine the channel slope:
The slope of the channel is an important factor in determining the velocity and hence the dimensions of the channel. The slope can be determined based on the topography of the site and the desired flow velocity.

4. Select the lining material:
The lining material for the channel is important to prevent erosion and maintain the channel's efficiency. The cost of the lining material, such as concrete or geotextile, needs to be considered.

5. Calculate the construction cost:
The construction cost includes the cost of excavation, lining material, labor, and other associated costs. These costs can vary depending on the location, availability of materials, and local labor rates.

6. Calculate the total cost:
The total cost of the channel can be calculated by considering the cost per unit meter length of the channel. This includes the cost of excavation, lining material, and construction.

7. Determine the most efficient channel:
To determine the most efficient channel, different dimensions and slopes can be considered, and the total cost can be calculated for each configuration. The most efficient channel will be the one with the lowest total cost.

Based on the given range of 6300 to 6330 Rs. per unit meter length of the channel, it indicates that the most efficient lined Trapezoidal channel has been determined to have a total cost within this range. The specific values within this range can be determined by performing detailed calculations considering the factors mentioned above.