My company operates and maintains sewer systems including lift stations. The arrangement you describe is called a "duplex" system - one pump is called "simplex".
Just a few of the myriad things that can go wrong in a lift station:
Panels corrode, internal components wear and corrode, if you have grinder pumps the cutting surfaces will wear, pumps need to be matched to each other and to the panel, otherwise you will have problems if the relays or capacitors are mismatched, sand can enter the system and prematurely wear your pumps out, infiltration can be a problem, check valves can clog or break, floats go bad or stick or get hung up, people flush things into toilets that they should not and it causes major problems in the lift station. THESE THINGS ARE ALL GUARANTEED TO HAPPEN AT ABOUT 1:00 IN THE MORNING IN A DRIVING SLEET-STORM ON CHRISTMAS EVE OR SOMETHING LIKE THAT.
On the other hand, you might have very little problem with your lift stations. Preventative maintenance is your friend - stuff you can do when the weather is nice.
Best thing you can do is keep a good log book at your LS and write down everything you do every time you open it. Include pump hours. Do a draw-down test on each of the pumps, know what the pump curve specs are. Try to keep a good spare pump, a float, and some panel components on hand. Check the station visually once a month whether you need to or not. Pull the pumps once a year whether they need it or not, clean them visually inspect them. Check the amp-draw of your pump motors regularly and write it down in your log. make sure you can power the lift stations in an emergency power outage via generator plug. Only do this if you understand how to do it safely.
If you have a licensed operator taking care of your permit, then dealing with your lift stations should be part of his responsibility. If you are doing this yourself, then you might seek out a local maintenance contractor who can respond in emergencies.... it never hurts to have someone available who can give you a hand when you are in a bind.