help with project of reading and searching big log file

[korenron]

Hello ,
I have a log file that in the end of the day get to ~ 6GB of text
now I want to be able to cut from it a certion windows of time
for example
from 08:00:00 -- until 08:15:00

I have checked and in 15 min I have a around 1.5 milion lines (1,500,000)
when I run the code in the morning , when the log file is less then 1GB - everything is working .

when I run the code in the end of the day (when the log is more then 5GB)
It get stuck , sometime I get on my computer Memory error

and when I try to search another later window (7:00pm-7:20pm ) it can take more then 3 min before it get stuck

my question is
what can I do to make this run better ? faster ?
can pythion handale this amount of data?

this is the function

def FilterLogFile(StartDate, EndDate):

    StartDate = datetime.datetime.strptime(StartDate, '%d/%m/%Y-%H:%M:%S')
    EndDate = datetime.datetime.strptime(EndDate, '%d/%m/%Y-%H:%M:%S')
    EndDate = EndDate.strftime('%d/%m/%Y-%H:%M:%S')
    StartDate = StartDate.strftime('%d/%m/%Y-%H:%M:%S')
    StartDate = str(StartDate)
    EndDate = str(EndDate)
    print(StartDate)
    print(EndDate)
    count = 0
    StartLine = 0
    EndLine = 0
    FullLogFile = open('/home/pi/logs/java.txt', 'r')
    Lines = FullLogFile.readlines()   ###------->>>> this part take to much time when it doens't stuck "Memory Error"
    FullLogFile.close()
    for line in Lines:
        count += 1
        if StartDate in line and StartLine == 0:
            print("Start Line {}: {}".format(count, line.strip()))
            StartLine = count
        if EndDate in line and EndLine == 0:
            print("End Line {}: {}".format(count, line.strip()))
            EndLine = count
        if StartLine != 0 and EndLine != 0:
            break  ## to stop the scan when he get to the wanted end time , no need to scan after the wanted time 

    count = 0
    print('start line is %d , end line is %d' % (StartLine, EndLine))
    print('total number of line is  %d' % (EndLine - StartLine))
    with open(OutputFile, 'w') as f:
        for line in Lines:
            count += 1
            if StartLine <= count <= EndLine:
                f.write(line.strip() + "\r\n")
    
    
    return OutputFile

Thanks,
maybe to read