nikiiiva - Welcome to the forum -
From the your statement that you have an XGA screen from T60 (and you are considering a Sharp LQ150U1LW22 LCD), I take it your R61i is a 4:3 Non-widescreen version - Model type: 894x.
I am not sure if the Sharp LQ150U1LW22 LCD is compatible with ThinkPad's that use 15.0" 4:3 LCD's, as there could be minor pin connector differences and if that is so may damage your R61i's motherboard. However if you want a UXGA LCD panel within your R61i, you could an IPS/FlexView BOE-hydis HV150UX1-100 - FRU: 13N7076 which was found in the 15.0" T60's - I have one installed in an R61i - works with no problems
You also have the choice of the following 15.0" 4:3 SXGA+ panels:
LG-Phillips - 15.0-in. SXGA+ IPS - FRU: 13N7078
BOE Hydis - 15.0-in. SXGA+ IPS - FRU: 13N7196
Samsung - 15.0-in. SXGA+ - FRU: 13N7128
LG-Phillips - 15.0-in. SXGA+ - FRU: 42T0350