Don't worry man, I just did a 15+ hour replay of Castlevania SoTN on my 60" through an OSSC when the room right next door is full of Sony BVM and PVM monitors (including a huge 32" PVM), it's sometimes just easier (and preferred) to play on a huge flatscreen at times.
If you're looking for around 40" I would look at the TCL 43" 5-Series. It's ~$399 I believe. The larger 55" is ~$699 ChuChuFlamingo mentioned and is their top-tier set (well, 2nd best as their 65" for a grand has slightly better features/specs). Some people have complained about banding on the newer sets so I would buy it from a brick and mortar store that will let you return it just in case you get one of those rare sets with a problem (which FYI, TCL's customer support seems to be very good and sending out technicians to look at any problem sets so no matter what you'll probably be taken care of).
There are other brands of course, but you mentioned budget and low lag, and nobody is really competing with TCL on a dollar-for-dollar basis in even the most remote sense (they really are a bargain).