From Findmypast:
Britain: outbound passenger lists 1890-1960

Name:Samuel LEESE
Date of departure:28 March 1906
Port of departure:Liverpool
Passenger destination port:Philadelphia, USA
Passenger destination:Philadelphia, USA
Date of Birth:1903 (calculated from age)
Age:3
Marital status:
Sex:Male
Occupation:Child
Passenger recorded on:Page 14 of 36

The following people with the same last name travelled on this voyage:
Robert A LEESE | Page 14 of 36
Thomas LEESE | Page 14 of 36

Ship: MERION
Official Number:
Master's name: J B Hill
Steamship Line: American Line
Where bound: Philadelphia, USA
Square feet: 35993
Registered tonnage: 7459
Passengers on voyage: 1973

The scan shows no.14768 Robert A Leese Lab [age] 29
Thomas Wife 27 [Meant to be Thomas child?]
Samuel Child 3

Under "English" passengers [English, Scotch, Irish, Foreigners].
.................................
Name:Eliz A LEICE
Date of departure:5 March 1914
Port of departure:Liverpool
Passenger destination port:Boston, USA
Passenger destination:Boston, USA
Date of Birth:1896 (calculated from age)
Age:18
Marital status:
Sex:Female
Occupation:Domestic
Passenger recorded on:Page 1 of 38
Ship: ALAUNIA
Official Number: 135513
Master's name: A H Rostron
Steamship Line: Cunard
Where bound: Boston, USA
Square feet: 16018
Registered tonnage: 8260
Passengers on voyage: 1133
....................
Name:Thomas LEESE
Date of departure:27 October 1927
Port of departure:London
Passenger destination port:Sydney, Australia
Passenger destination:Sydney, Australia
Date of Birth:1897 (calculated from age)
Age:30
Marital status:Married
Sex:Male
Occupation:Potter [The scan wasn't available to see whether this was supposed to be porter.]
Passenger recorded on:Page 26 of 31

The following people with the same last name travelled on this voyage:

Mrs Emily LEESE | Page 26 of 31 [wife, 28]
Thomas LEESE | Page 26 of 31 [8 months]

Ship: BALLARAT
Official Number: 145596
Master's name: Captain John W Parker
Steamship Line: P. & O. Australia Via The Cape Service
Where bound: Australia
Square feet: 28135
Registered tonnage: 7928
Passengers on voyage: 911

.................................
Name:Edith LEECE
Date of departure:11 October 1923
Port of departure:Liverpool
Passenger destination port:Quebec, Canada
Passenger destination:Quebec, Canada
Date of Birth:1900 (calculated from age)
Age:23
Marital status:
Sex:Female
Occupation:Domestic
Passenger recorded on:Page 5 of 25
Ship: MONTROSE
Official Number: 145919
Master's name: Capt Parry
Steamship Line: Canadian Pacific
Where bound: Montreal, Canada
Square feet: 14583
Registered tonnage: 9823
Passengers on voyage: 824

You need to check US and Canadian census records for place of birth to see whether the ones who went there were the Leeces you are looking for.

There are many other possible son Thomas Leece listings, often with no ages given.

Sue