As noted in Lexorank support Tools page :

A rebalance will start (within a minute) and complete the failed balance, majority of issues with long rank values will be rebalanced. At this point there may still be issues with long rank fields, and a second re-balance may be required. After the completion of a second rebalance, the rank system will enable ranking operations.

I many cases the Rank Rebalance does not Occur, and the max_rank_string_length value increases causing high CPU load on the system whenever an issue with a large value is referenced, either in an agile board or the ticket directly, in many cases leading to a System outages due to load.
If a timeout occurs you will see the following in the logs:

[greenhopper.customfield.lexorank.LexoRankIndexer] Could not retrieve LexoRank value for issue[id=jiraIssueID]. Indexing max LexoRank value instead.

Majority of the time no indication of the issue are visible until timeout occurs.

UPDATE:

We have been able to narrow this down to the following two conditions:

• max_rank_string_length is high
• Number of issues in Agile field_id Also HIGH

When both of these values are at increased levels the performance hit occurs until the max rank value is balanced.

• EXE. a heavily used Agile Board

Workaround:

Follow the steps in this Knowledge Base Article.