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Hello and sorry you're having problems. The red light under "Lamp" being lit does indeed mean that the Lamp in the set needs to be replaced. The TV will not turn on, or off when the lamp has failed- this is a diagnostic built into the set to prevent the set from powering with a bad lamp. The Lamp for your set can be purchased at the link below:
Also, below is the link to your Owner's Manual, and instructions on replacing the lamp are on page 93:
If you need further assistance let me know. Please do not forget to click a POSITIVE RATING before you go- as it's how I am credited for my work. You can follow up at any time, at no additional cost.