search tries to update the index, while it is locked by another process.
If this is not caused by a sudden restart (keeping the lock file locked) and there are either multiple servers processing the index (in web farm scenarios make sure, search index is assigned to a single web server), there must be an external service blocking the file, e.g. backup, virus scan.

I think that this happened when the installation was moved from one server to a new one.

Also I get an error loading the Search PB page when I try to go to Basic Settings.

Would deleting the Write Lock file be a solution?

yes, you should try deleting the lock file in /app_data/search.

Hmmm ...

Here is the entire traceback:

Message:Lock obtain timed out: NativeFSLock@F:\npiDNN2\App_Data\Search\write.lock

StackTrace:

at Lucene.Net.Store.Lock.Obtain(Int64 lockWaitTimeout)
at Lucene.Net.Index.IndexWriter.Init(Directory d, Analyzer a, Boolean create, IndexDeletionPolicy deletionPolicy, Int32 maxFieldLength, IndexingChain indexingChain, IndexCommit commit)
at Lucene.Net.Index.IndexWriter..ctor(Directory d, Analyzer a, MaxFieldLength mfl)
at DotNetNuke.Services.Search.Internals.LuceneControllerImpl.get_Writer()
at DotNetNuke.Services.Search.Internals.LuceneControllerImpl.Delete(Query query)
at DotNetNuke.Services.Search.Internals.InternalSearchControllerImpl.DeleteSearchDocumentInternal(SearchDocument searchDocument, Boolean autoCommit)
at DotNetNuke.Services.Search.SearchEngine.DeleteRemovedObjects()
at DotNetNuke.Services.Search.SearchEngineScheduler.DoWork()

And there is no file F:\npiDNN2\App_Data\Search\write.lock

File F:\npiDNN2\App_Data\Search\write.lock is temporary and deleted upon app restart.
The Lucene timeout indicates that DNN tries to modify or delete the file, but is unable, because it is locked by a different process - now you need to find out, wich process. Is there anything in the windows system logs?