How much time should I give myself to catch a connecting flight at Changi Airport without baggage?

Arrival

Just like what Eric has said, the worst case is if your AirAsia flight arrives at the furthest gate from immigration. Unfortunately, if I fly with AirAsia or Jetstar most certainly I will depart/arrive from far gates (C16-19, C24-26, D35-38, D46-49). In addition to that, when you arrive to Singapore sometimes there will be a random check on handcarry item (I encountered it a few times, and perhaps due to Jakarta bombing last week there will be checking again).Walking takes around 10 minutes, x-ray check takes at most 5 minutes, immigration takes around 10-15 minutes. So you will spend around 30 minutes for your arrival.

Transfer

This depends on your luck. You will have to take Skytrain from T1 to T3 (go up to departure hall first). If you arrive from C concourse, you will be lucky because C is nearby Skytrain to T3; but if you arrive from D concourse (which is close to T2) you have to walk quite longer. Worst case will take you around 10 minutes until you reach Terminal 3.
When you arrive at Terminal 3, the closest check-in row is row 11 while Lion Air is located at.... row 1. So you have to walk to the other end of departure hall. Will take you around 3-5 minutes and in total to change terminal you need around 15 minutes.

Departure

I've flown with JT163 (Lion Air's Singapore - Jakarta afternoon flight) for several times. Checking-in your flight will not be very long as Changi is very efficient, so I think 5-10 minutes must be enough for check-in. The bad thing is about gate. The flight is often (if not always) placed at A16-A20 gates, and walking from departure immigration to the gate can take 15 minutes alone. So far (surprisingly) I have never experienced any delay with this flight, so if you often hear about Lion Air's bad reputation in terms of on-time performance I don't think you should expect that in this flight. I guess for departure you need 30 minutes.

Of course my approximation is a bit exaggerated, but it is better to spare some time right? So I recommend you to take the earlier flight. Good luck, and I hope your trip will go smoothly :)