Having a look at
No 1 lounges, they differentiate between their products:
Is there a dress code?
Yes, we have a dress code in place to ensure a premium lounge experience for all our guests. It differs slightly by lounge brand:
Clubrooms or No1 Lounge guests
We ask all of our guests to wear smart-casual clothing.
We reserve the right to refuse admission to anyone wearing clothing which we deem to be unsuitable. This may include themed or fancy dress outfits, clothes with slogans that may cause offense, replica sports kits, beach flip flops, clothing that exposes midriffs or upper thighs, or bare shoulders on men. We also ask that guests do not wear tracksuits while in the lounge – we appreciate that people like to travel comfortably and so welcome guests to change when departing the lounge.
My Lounge guests
We ask all of our guests to wear smart-casual clothing. We reserve the right to refuse admission to anyone wearing clothing which we deem to be unsuitable. This may include themed or fancy dress outfits, replica sports kits, clothes with slogans that may cause offense, clothing that exposes midriffs or upper thighs, or bare shoulders on men. We reserve the right to refuse admission to anyone wearing clothing which we deem to be unsuitable.
But what you are planning is fine. No 1 Lounge is the better of the paid options at T3 that I saw, but be aware that they used to turn away a lot of pass holders when I was travelling last year at busy times. But the CX lounge wasn't open at the time so it may have improved. You can guarantee entry in advance for an additional £5 fee bookable in advance on their websites.