Should I use SQL Server DMVs with NOLOCK
What are the consequences of reading DMVs in a production live OLTP database?


Negligible as far as my experience goes. DMV's as the name suggests are basically views or functions ( like sys.dm_db_index_physical_stats ) which get information from various caches and system tables. DMV's are very light and read data from caches. They do not cause blocking and depending on amount of data you need to fetch they very very quick. The point here is always only query data from caches which you actually need.

You may use NOLOCK hint in your DMV query you would see some people using it but frankly I do not see much of need to use it with DMV's. Its function though still remains same. So when you use NOLOCK hint you say to SQL Server that give me the data I am asking no matter what is state of the data is. It may have been changed and yet not committed so you get "dirty" data. NOLOCK hint avoids select queries taking shared lock while reading data. The drawbacks are many


  Additionally, with NOLOCK, is there higher chance query will continue forever in high volume environment since I am not locking rows, pages, and things will continue be added into DMV TableView?


Query will only continue for duration until it finishes its task, unless you run a never ending loop. The NOLOCK only ensures that query is minimally blocked and also note that when using NOLOCK if required other locks like schema stability  are taken