If the big ropway behind the Grand Hotel Praha is not running then you may consider taking the gondola up to Skaluate Pleso, where you can change to another ropeway which takes up on top of the mountain.
Since we travelled pre-season we were not able to take this trip as the gondolas/ropeways were closed until the beginning of June for maintenance.
If there is no train running when you want to travel you may want to check the bus timetable at the nearby bus station. We took the bus back to Poprad which cost 25 SKK compared to 30 SKK by Tatra train. The bus is very quick and part of the downhill journey from Stary Smokovec was a straight road which is quite impressive when you sit in the front.
We arrived in Lomnica from Zakopane in Poland, a journey which took about 1 hour and 10 minutes and cost 14 Zloty each. There are 2 mini buses a day to and from Zakopane and there are regular stops at most of the High Tatra towns such as Lomnica, Stary Smokovec and Horne Smokovec before the final stop in Poprad. I think this is the best way to get here from Zakopane by public transport as otherwise you have to take a bus to Lysa Polana at the border and then another bus onwards from there though you'll probably have to wait between journeys as the buses aren't too frequent.
At Tatranska Lomnica there are regular buses to nearby towns. For anyone interested in going to Levoca there a couple of buses which go direct. We took one of these, at 9.45 am, when we moved on from Lomnica - it took about an hour and a half and the cost was under 100 SKK.
There is also a train station in Lomnica with frequent electric trains to Poprad and the Smokove resorts nearby. A one way ticket to Stary Smokovec cost only 28 SKK.
The little trains (more like trams really) often give excellent views. The connect well even if they are on the slow side. Fares are very cheap.
Even better, they connect down to Poprad which is likely to be the place you would approach the Tatras from.
Train enthusiasts sometimes "Do" the entire system - but it would take you all day.
You can reach Tatranska Lomnica from Poprad by changing trains in Stary Smokovec. They always connect there. They run about hourly. The tickets you can buy in the old station building opposite.
From/to Poprad there is another option. You can take the diesel train to Studeny Potok in the lowland and from there a local train either to Poprad or to Kezmarok.