If your LSI (I've NFI what it is - but I assume some serial bus) needs a lot of clocks to perform an action, it may be better to perform the LSI transfer completely asynchronously and have the Avalon master (eg nios) either poll for completion or (if very very slow) take an interrupt.
That way you don't completely stall the nios cpu while your slow LSI transfer takes place, and you'll have complete control of the number of words read/written from the LSI slave in one transfer.
The nios cpu can only do burst transfers for cache line fill/write, but doesn't normally have that enabled because it isn't necessary for internal memory or SDRAM/DDR.