It is the first time the Capital outfit have tasted success at the Arlington track and completed a fine weekend for the blue and gold having saw off reigning champions Leicester Lions 49-40 24 hours beforehand at Armadale on Friday night.
Skipper and No.1 Sam Masters top scored with 13 from his five rides but for 20-year-old Lawlor, his four point-haul, including a first race win in Monarchs colours, was every bit as important to the team's triumph on the southeast coast.
"It was great to get my first race win for the Monarchs and I was buzzing all the way home – it was like I had won a Grand Prix," Lawlor said. "I really needed that on Saturday night. I have had a pretty c**p start to the season and I think I've just expected a bit too much. I went well in 2019 and was competing against some really good riders so I think I'm just putting too much pressure on myself.
"I started doubting myself too and even thought do I want to do this? But I'm just going to enjoy it and I went out in my first race on Saturday and bang I was gone. I know what I am capable of but because I've had such a bad start, I was just so happy to get a win.
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"Halfway through the meeting I went up to Sam Masters and I said 'I bet they [Eastbourne] thought they were going to give us a spanking' but he just looked at me as if I had two heads, so confidence is key.
"Speedway is all about being mentally tough. I didn't do a whole lot more in the rest of my races but I just felt more confident. I was making starts. Because I'm riding at No.6 I have some real hard races.
"I feel all the time I need to win so I just need to relax a little more. I've had problems with my wrist but hopefully that's getting better. I honestly think we're a really strong side and definitely contenders to win the league."
The Monarchs provided the first six race winners of the meeting on Saturday night and found themselves six points ahead 21-15.
This forced the hosts into a tactical switch in heat seven. However, it failed to pay dividends as despite Richard Lawson finishing first, Tom Brennan, who had replaced reserve Jason Edwards, trailed in last place behind Australian duo Josh Pickering and Kye Thomson.
But the Eagles tied the meeting up with a 4-2 and 5-1 in heats eight and nine only for Monarchs to restore their advantage once more with a 5-1 of their own from Pickering and Thomson.
The visitors led 43-41 going into the final heat and just as it looked as if the Eagles would steal a last-gasp win with Lawson and Kyle Newman out trapping Masters and Pickering, Newman suffered an engine failure to allow the Monarchs pair through to seal a narrow win.