GS300 2007 Gearbox advice

[Blanken]

Hi all

I've had my GS300 for about 2 months now, it's done 110k miles. 

I've noticed whenever I shift from reverse to drive or vice versa it can jolt a bit sometimes and I feel like it's floating between gears sometimes when accelerating, and it's a bit reluctant to downshift at times and will stay in low RPM unless I blip the throttle or almost floor it. Now I haven't driven any other lexus's so I don't know how it should change gears to be able determine what it should be like. 

And just recently two times it hasn't been willing to go into 6th on a cold day until about 3-5 minutes into the drive. 

So I don't know whether it's something a gearbox oil change / flush would fix or help towards making it better. Anyone got any advice what the best cause of action would be. Or know any good garages near Liverpool (don't mind a long ish drive to get to a good place) and what price would I be looking at if best case it's fixed with just a fluid change. 

Or if it's something that's not too complicated to get my family mechanic to have a look at. 

Thanks in advance. 

[Mihanicos]

Change the transmission filter and oil with original parts. If the filter is made of fine steel mesh ( Japanese market models ) no need to change the filter. Make sure you check the oil level when its temperature is between 30C and 40C.

Chris.