Why not put your bags in the rafts of luggage lockers in Lucerne's train station (in the basement), then hop the boat from across from the station to either Vitznau or Weggis and take from the former a mountain train to Rigi Kulm the summit or from Weggis an aerial cable car to the same place?

Then reutrn via taking the train to Arth-Goldau from the summit to change to a quick train back to Lucerne.

If going onto Interlaken you then from Lucerne take the very scneic Brunig Pass rail line - the only Swiss Federal mainline to have to use cogs and cog wheels to safely negotiate prodigious ascents and descents - take the lovely rail line, which before reaching Interlaken lovingly tracks along the shores of Lake Brienz to Interlaken-Ost, from where trains into the maountain depart.

so though taking a train from Zurich to Arth-Goldau may make a quicker trip to the Rigi summit the overall experience of boat on fjord-like Lake Lucerne is tremendous and a Swiss Pass if you have one is valid on the boats and trains to the summit.

For info on lockers in Arth-Goldau I'd scour www.sbb.ch - Swiss Federal Railways site - and for lots of great info on Swiss trains, lake boats on lake Lucerne, etc I always highlight these IMO superb sites - www.swisstravelsystem.com; http://www.budgeteuropetravel.com/id3.html; and www.ricksteves.com.

according to www.sbb.ch Arth-Goldau has a luggage facility open Mon-Fri 7am to noon and 1-6:15pm (closes at 4:15pm Sat Sun) but there is no mention of lockers - but there is a place to store bags at this manual luggage desk (and you could have your bags sent onto Interlaken with the Swiss Railways program - check them in Zurich and having them waiting in Interlaken.

There are lockers at Ath-Goldau railway station - see http://www.sbb.ch/content/sbb/en/desktop/bahnhof-services/am-bahnhof/standort/bahnhoffinder.html?_charset_=utf-8&stationname=Arth-Goldau -. There area always staff members on the plattforms when a train arrives. Just ask them where the lockers are.
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