I'm trying to 'gray' water my lawn, but my washer is on an interior wall.

Assuming I don't route it UPhill, how long a hose can I connect to the washer,
Without overtaxing the pump?

You might do better to pump the water to a rain barrel positioned as close to the washer location as possible and then allow gravity to do the rest of the work with soaker hoses or drip irrigation hose.

Also, when reclaiming water from a clothes washer, make sure you use a High Efficiency/Low Phosphate detergent.

As long as you maintain the same size hose as the one that comes out of the washer you should be OK. You can not run the line uphill at all, stay flat or maintain a slope. Before you do any of this I suggest you dump a bucket of your washer water on the same spot of the blawn several times and then compare it to the rest of the lawn. Washer detergent is petroleum based.