Along with the other suggestions, you might also want to post the values of the following configuration options:
page lock promotion HWM
page lock promotion LWM
page lock promotion PCT
row lock promotion HWM
row lock promotion LWM
row lock promotion PCT
lock scheme
If you identify a transaction running against a large table (e.g. >15000000 rows) then you could perhaps change the escalation so a full table lock is taken out, our use the granularity of the locking system to set that table first to perhaps DPL (data-page locking) instead of DRL (data-row locking) if that is the issue.
Tables can be changed to different locking schemes, even if the server-wide lock scheme is set differently.
Chris