REST API calls to retrieve threads return the data in 'pages'. The page size and page number can be specified when making the call:
http://lithosphere.lithium.com/t5/rest-api/bd-p/developers-rest-api?leaf-id=Board.threads#Board.threads
You can determine the total number of threads using /threads/count under the appropriate node. Simple maths will tell you how many pages you need based on the total count and the page size.
Custom components can take parameters:
http://lithosphere.lithium.com/t5/developers-knowledge-base/Passing-Parameters-to-a-Custom-Component/ta-p/88704
You can retrieve parameters in the URL from within your custom component:
https://lithosphere.lithium.com/t5/developers-discussion/Component-and-parameters/m-p/42432/highlight/true#M1141
This means you could create your own page number links, which include a page number parameter in the URL. That can be read by the custom component on the page in order to retrieve the corresponding data page from the REST API.