article : the

The nature of "television" in both sentence is identical. "Television" here is used as or means a broadcast medium, not a television set or home electrical appliance. So no article (the) is required.
1. He often appears on television but his name has slipped from my mind.
2. Lisa Wong is an actress. I like to watch her on television.I watch television at home every night. - this still means the broadcast.

Use "the" only if "television" in the sentence means the hardware/product/device you can touch and with physical feature that is placed in your home.

I want to change the old television to a 50-inch LCD TV.
He is glued to the television every night from 9:30-10:30 to watch his favorite show.

1. He often appears on X television but his name has slipped from my mind.
2. Lisa Wong is an actress. I like to watch her on X television.

on tv=上電視, the tv=嗰個電視機
in hospital=入醫院,in the hospital=喺1間醫院裡面,可能探朋友
因為the有特定指某一樣嘢,唔係是但1個,所以除咗the sun, the sea, the moon嗰類,習慣咗用嘅,其他唔係成日亂用

1. He often appears on the television but his name has slipped from my mind.

2. Lisa Wong is an actress, I like to watch her on television.