Terraform: Issue while reading value from aws ssm parameter store

I am looking to retrieve value from aws ssm paramter store and assigning to a varibale of type map

AWS SSM parameter store:
 
name: lambda_env
value: {"var1"="value1","var2"="value2","var3"="value3"}


variable.tf:

variable "lambda_env_vars" {
  type    = map(string)
  default = null
}


main.tf:

data "aws_ssm_parameter" "lambda_env" {
  name      = "lambda_env"
  
}

module "lambda" {
  source = "../modules/lambda/"
lambda_env_vars             =  tomap(data.aws_ssm_parameter.lambda_env.value)

}

terraform plan is giving below error:

**"Invalid value for "v" parameter: cannot convert string to map of any single type"**

It is working fine if I give direct value as

lambda_env_vars = tomap({"var1"="value1","var2"="value2","var3"="value3"})

The output of data.aws_ssm_parameter.lambda_env.value is as shown below

outputs:
aws_ssm_var = "{\"var1\"=\"value1\",\"var2\"=\"value2\",\"var3\"=\"value3\"}"

The data.aws_ssm_parameter.lambda_env.value is a JSON formatted string. You need to convert it to a map with the jsondecode function. tomap converts HCL2 types to a map.

lambda_env_vars = jsondecode(data.aws_ssm_parameter.lambda_env.value)