Lack of middleware application to support bi-directional integration between two separate systems, could arise difficulties such as:

1. Lack of Integration: Without middleware, the systems cannot communicate with each other, leading to a lack of integration and siloed data.

2. Data Inconsistencies: If data is entered or updated in one system, there will be no automatic updating of data in the other system, leading to data inconsistencies.

3. Increased Manual Effort: Without middleware, any data transfer or synchronization between the systems will require manual effort, which is time-consuming and error-prone.

4. Security Risks: If manual data transfer is used, there is a risk of data leakage or security breaches.

5. High Maintenance Cost: Maintaining and updating manual data transfer mechanisms can be time-consuming and expensive.

6. Inability to Scale: As the volume of data and transactions increase, manual data transfer mechanisms become increasingly difficult to manage and can result in delays and errors.

Overall, the lack of a middleware application can cause significant challenges for organizations, including data inconsistency, reduced efficiency, increased manual effort, security risks, high maintenance costs, and scalability issues.