I am afraid that this is not so easy. Functions of lincRNAs are far to be understood. There are some databases with already characterized functions like
http://www.lncrnadb.org/
You can also use gene expression data to check for co-expression networks and infer putative lincRNA functions.
I am afraid there isn't any database available for lncRNA - DNA interactions, but the NPInter database(http://www.bioinfo.org/NPInter/) offers about 60 entries about RNA-DNA interactions(lncRNA-DNA interaction included). Besides, I am trying to integrate a database of RNA associated interactions based on literature mining, but isn't finished yet. May helpful for you.
http://www.bioinfo.org/NPInter/
Article NPInter v2.0: An updated database of ncRNA interactions