DIAGNOSIS No, it's not normal. The battery should seat with a firm, positive click and have no play. This is either a new-tool shipping lock or a defective/misaligned latch.
FIX First, check for a small plastic shipping lock or tab on the battery slide rails. Remove it. Then, inspect the black battery release latch on the tool. Press it fully to ensure it's retracted, then try inserting the battery again with firm, even pressure.
IF THAT DIDN'T WORK Compare with another LXT tool if you have one. If the battery fits snugly elsewhere, the latch mechanism inside your new impact is defective. If the battery is loose in all tools, the battery casing is out of spec.
HEADS UP Do not use the tool with a wobbly battery connection. The intermittent connection can damage the tool's electronics and is a safety hazard. Return or exchange it while it's new.