You can add multiple applications to a single LCA and deploy the single LCA to the fresh install. You create an LCA through Workbench and deploy it to the new server with AdminUI.
https://helpx.adobe.com/pdf/aem-forms/6-2/WorkbenchHelp.pdf
Create an archive file 1) In the Applications view, right-click the application version and select Create AEM Forms Archive. 2) Select Create A New Archive File and click Next. 3) Select applications and/or assets to be included in the archive file. The following rules apply when selecting applications and assets: • To make a selection, select the check box beside a component. To deselect a component, select the check box again. • A shaded box indicates that child components are selected implicitly.
There are deployment APIs but it will likely take you longer to build an app to do this than to just select the apps. If you deploy apps on a regular basis it might might sense to expend the effort.