AVR assembly: Most fastest way to increment two combined bytes
Have a bit more trust in your compiler. Write the code in C, compile it and look at the disassembly. Unsure which toolchain you use, but avr-gcc creates pretty well optimized code.

lds     r24 , lowbyte   ; 2 clocks
lds     r25 , highbyte  ; 2 clocks
adiw    r24 , 0x01      ; 2 clocks - Add Immediate to Word (= 16 bit)
sts     lowbyte  , r24  ; 2 clocks
sts     highbyte , r25  ; 2 clocks


You can disassemble the .elf file with the following command (provided you use the gcc toolchain):

avr-objdump -C -d $(src).elf


BTW: You probably need to push the used registers to stack beforehand and pop them afterwards (2 cycles each). Also remember that an interrupt (including reti) lasts at least 8 clock cycles apart from the instructions being executed.

; TIMER1_OVF            ;  4 clocks
push    r24             ;  2 clocks
IN      r24 , SREG      ;  1 clock  - save CPU flags
push    r24             ;  2 clocks
push    r25             ;  2 clocks
; do the addition above - 10 clocks
pop     r25             ;  2 clocks
pop     r24             ;  2 clocks
OUT     SREG , r24      ;  1 clock
pop     r24             ;  2 clocks
reti                    ;  4 clocks
; total 32 clock ticks