Two thoughts for you in addition to dmckee's answer.
1) Andrew Murray's research group in Manchester has done some experiments on superelastic collisions of electrons with excited atoms, see for example here. In these collisions free electrons hit excited atoms and gain energy from the excitation energy of the atom. This is a difficult experiment - you need a nice laser system to make a large enough population of excited atoms to make it possible.
2) You mention losing energy as 'heat'. Energy loss to heat is particularly relevant to systems where the excited atoms (or molecules) are in liquid or solid. Effectively the excitation energy is converted by collisions with neighbouring atoms (or molecules) into vibrational / rotational motion, which goes into heat. This is relevant to Kasha's rule in classical photochemistry. Kasha's rule applies to molecules in liquids (or solids).
So in the case of the discharge lamp you are thinking of the excited atoms are in a gas phase environment and the likelihood of losing excitation energy to heat will depend on the rate of collisions and, hence, the gas pressure.