The suggestion on the trouble code lights is spot on. The furnace is sensing a failure in the event chain leading up to ignition "go". After you get the trouble codes google them along with your Lennox furnace model. Trust me you are not alone on this and there will be help available. In some cases you will find YouTube videos that are very helpful.
There are pressure sensors that are used to sense the gas purge flow from the fan/draft inducer. These must feel the fan in order to let the gas valve open. The sensors are not that expensive and are easy to replace. There are tubes that go from the fan to the sensors and they could be loose.
The draft inducer could very well be the culprit. Make sure that the inducer is running at full speed with no bearing squeal.
I recently trouble shooted my daughter's 6 year old Goodman furnace and the code was telling us that the pressure sensors had failed. It turned out that the sensors were ok but the draft inducer was not running at full speed due to a bad bearing. Penetrating oil got it running for a few days while we ordered a new inducer (about $110.00). A simple 15 minute installation and it was like new again.
One thing I discovered was that Goodman somehow won't replace the draft inducer under their 10 year parts warranty. I don't think I will ever buy one of their furnaces.