buildspec.yml if you want to deploy using AWS CodeBuild (would be an unusual flow):

---
version: '0.2'
phases:
  install:
    commands:
    - echo Entered the install phase...
    - npm install --global lerna
    - lerna bootstrap --concurrency=1 -- --production
  build:
    commands:
    - sam build
    - sam deploy --stack-name stackoverflow-stack --capabilities CAPABILITY_IAM --no-fail-on-empty-changeset
      --s3-bucket your-bucket-name-here --parameter-overrides AppId=your-app-id-here

buildspec.yml if you only want to produce a CloudFormation template file which you can directly deploy (using CodeDeploy or other means). It is almost the same as what you already have, with the following difference:

• Adds sam build
• Uses sam package instead of aws cloudformation package. sam package uses .aws-sam/template.yaml (output of sam build) instead of template.yaml as the first default.

---
version: '0.2'
phases:
  install:
    commands:
    - echo Entered the install phase...
    - npm install --global lerna
    - lerna bootstrap --concurrency=1 -- --production
  build:
    commands:
    - sam build
    - sam package --s3-bucket your-bucket-name-here --output-template-file
      template-export.yml
artifacts:
  files:
  - template-export.yml

Edit2: OP's build project was created by Lambda applications. The build project uses aws/lambda/nodejs:10-1.0 which has two issues:

• The SAM CLI version is outdated
• Java isn't installed because the image is meant to be used for nodejs based Lambda functions. Java is required to build the Java based AWS Lambda function

The following buildspec.yaml can be used to fix both these issues:

---
version: '0.2'
phases:
  install:
    commands:
    - echo Entered the install phase...
    - npm install --global lerna
    - lerna bootstrap --concurrency=1 -- --production
    - yum install -y amazon-linux-extras which
    - amazon-linux-extras install java-openjdk11
    - pip install aws-sam-cli --upgrade
  build:
    commands:
    - sam build
    - sam package --s3-bucket cf-templates-fgoi5xu7d2hs-us-east-1 --output-template-file
      template-export.yml
artifacts:
  files:
  - template-export.yml

There are Docker images for Java and NodeJS. I would suggest to use Docker Images as the base for your lambdas.

For Java

Example Dockerfile below:

FROM public.ecr.aws/lambda/java:11

# Copy function code and runtime dependencies from Gradle layout
COPY build/classes/java/main ${LAMBDA_TASK_ROOT}
COPY build/dependency/* ${LAMBDA_TASK_ROOT}/lib/

# Set the CMD to your handler (could also be done as a parameter override outside of the Dockerfile)
CMD [ "com.example.LambdaHandler::handleRequest" ]

Example Gradle task definition to prepare the runtime dependencies:

task copyRuntimeDependencies(type: Copy) {
    from configurations.runtimeClasspath
    into 'build/dependency'
}

For NodeJS

Example Dockerfile below:

FROM public.ecr.aws/lambda/nodejs:12

# Copy function code
COPY app.js ${LAMBDA_TASK_ROOT}

# Set the CMD to your handler (could also be done as a parameter override outside of the Dockerfile)
CMD [ "app.handler" ]

To test both the images locally

To build your image:

docker build -t <image name> .

To run your image locally:

docker run -p 9000:8080 <image name>

In a separate terminal, you can then locally invoke the function using cURL:

curl -XPOST "http://localhost:9000/2015-03-31/functions/function/invocations" -d '{"payload":"hello world!"}'

Reference:

• https://gallery.ecr.aws/lambda/nodejs
• https://gallery.ecr.aws/lambda/java

You can also try to create multi layer lambda. Not sure if it works.