If the bath is higher than the lawn and if the subsoils are sandy, draining to the lawn is a good idea imo ... you could have a 10m or so length of perforated hose snaking around the lawn to distribute the water better ... if you or your partner are particularly hirsute then a cleanable filter betwixt bath and hose would be a good idea.
If the subsoils are clayey I can help you as well but I need to know more details. I am a geotechnical engineer.
